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Anonymous1502
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Can someone please tell me how to solve these questions,I have no idea what steps I should take,any help would be much appreciated.

7t+6=492t
(7 to the power of t+6 is equal to 49 to power of 2t)
9 y+8 = 27 y+5
(9 to the power of y+8 is equal to 27 to the power of y+5)
4r5 + 7=100
(4r to the power of 5 + 7 =100)
s-5=4
(s to the power of -5 is = to 4
simplify: (2√x)4
———
8x

(2 root x to the power of 4 over 8x)
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fliscia
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For these you need to make the base numbers equal eachother, so for example 2^2 = 4, so if you had 4^t+1 = 2^t you could do (2^2)^t+1 = 2^2t+2 = 2^t, therefore 2t+2 = t, t = -2. This can be applied to powers of 3 so 2^3 = 8.

For the later questions if x^2 = y then the square root of y is x and vice versa.

For the last one remember that the square root of x is x^0.5.
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M4cc4n4
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Um

7^(t+6) = (7^2)^(2t)

t+6 = 4t
6 = 3t
T = 2
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kimberry50
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i just make the bases the same on each side which i call "factoring the powers" as mathematical as that sounds..
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Anonymous1502
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(Original post by fliscia)
For these you need to make the base numbers equal eachother, so for example 2^2 = 4, so if you had 4^t+1 = 2^t you could do (2^2)^t+1 = 2^2t+2 = 2^t, therefore 2t+2 = t, t = -2. This can be applied to powers of 3 so 2^3 = 8.

For the later questions if x^2 = y then the square root of y is x and vice versa.

For the last one remember that the square root of x is x^0.5.
For this question: 4r5 + 7=100

I took away 7 and ended up with:

4r^5 =93

And Im not sure what to do next or even if Im approaching the question right, could you please give me a clue for this question?
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ManLike007
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(Original post by Anonymous1502)
Can someone please tell me how to solve these questions,I have no idea what steps I should take,any help would be much appreciated.

7t+6=492t
(7 to the power of t+6 is equal to 49 to power of 2t)
9 y+8 = 27 y+5
(9 to the power of y+8 is equal to 27 to the power of y+5)
4r5 + 7=100
(4r to the power of 5 + 7 =100)
s-5=4
(s to the power of -5 is = to 4
simplify: (2√x)4
———
8x

(2 root x to the power of 4 over 8x)
7^{t+6} = 49^{2t}
9^{y+8} = 27^{y+5}

For both of these questions, simplify both sides to the same base i.e 36 \equiv 6^{2}

For 4r^{5}+7=100, move the unknowns to one side so r^{5} = ....
Now to remove the power, you flip the power to the other side i.e a^{3} = 27 \Rightarrow a=27^{\frac{1}{3}}
So going back to the question, apply this to find the value of r.

For s^{-5}=4, now you must know that x^{-a} \equiv \frac{1}{x^{a}} so use this method as well as the method I told you previously about flipping powers to the other side to find your value of s.

For \frac{(2\sqrt x)^{4}}{8x}, you must know that \sqrt x \equiv x^{\frac{1}{2}}.

So you have \frac{(2x^{\frac{1}{2}})^{4}}{8x  },

Then apply the power of 4 (i.e (ab)^2 \equiv a^{2}b^{2}) then simplify this using the denominator.
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fliscia
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(Original post by Anonymous1502)
For this question: 4r5 + 7=100

I took away 7 and ended up with:

4r^5 =93

And Im not sure what to do next or even if Im approaching the question right, could you please give me a clue for this question?
If 4 of r^5 is 93, then what is r^5?
Furthermore if r times itself 5 times is x, then what is r?
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Anonymous1502
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(Original post by fliscia)
If 4 of r^5 is 93, then what is r^5?
Furthermore if r times itself 5 times is x, then what is r?
I solved it now,I took away the 7 and divided by 4 so I had 93/4 = r^5

then 23.25= r^5 then I did to the power of 5 root 23.35 and got 1.88 to 3sf.
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fliscia
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(Original post by Anonymous1502)
I solved it now,I took away the 7 and divided by 4 so I had 93/4 = r^5

then 23.25= r^5 then I did to the power of 5 root 23.35 and got 1.88 to 3sf.
Yep that's correct!
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Anonymous1502
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(Original post by ManLike007)
7^{t+6} = 49^{2t}
9^{y+8} = 27^{y+5}

For both of these questions, simplify both sides to the same base i.e 36 \equiv 6^{2}

For 4r^{5}+7=100, move the unknowns to one side so r^{5} = ....
Now to remove the power, you flip the power to the other side i.e a^{3} = 27 \Rightarrow a=27^{\frac{1}{3}}
So going back to the question, apply this to find the value of r.

For s^{-5}=4, now you must know that x^{-a} \equiv \frac{1}{x^{a}} so use this method as well as the method I told you previously about flipping powers to the other side to find your value of s.

For \frac{(2\sqrt x)^{4}}{8x}, you must know that \sqrt x \equiv x^{\frac{1}{2}}.

So you have \frac{(2x^{\frac{1}{2}})^{4}}{8x  },

Then apply the power of 4 (i.e (ab)^2 \equiv a^{2}b^{2}) then simplify this using the denominator.
Thank you for your help but Im still struggling to solve:
(2√x)4
———
8x

Could you please tell me how you got 2 to the power of 1/2 to the power of 4?
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ManLike007
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(Original post by Anonymous1502)
Thank you for your help but Im still struggling to solve:
(2√x)4
———
8x

Could you please tell me how you got 2 to the power of 1/2 to the power of 4?
As I said, you need to know that \sqrt x is the same as x^{\frac{1}{2}}.

The numerator now becomes (2 \times x^{\frac{1}{2}})^{4} because before you had (2 \times \sqrt x)^{4} but we need this in terms of powers to simplify this.

Now as I said (ab)^2 is the same as a^{2}b^{2}

So to simplify the numerator, (2 \times x^{\frac{1}{2}})^{4} \Rightarrow (2)^{4}(x^{\frac{1}{2}})^{4}

Can you work from here? \frac{(2)^{4}(x^{\frac{1}{2}})^{  4}}{8x}
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Anonymous1502
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(Original post by ManLike007)
As I said, you need to know that \sqrt x is the same as x^{\frac{1}{2}}.

The numerator now becomes (2 \times x^{\frac{1}{2}})^{4} because before you had (2 \times \sqrt x)^{4} but we need this in terms of powers to simplify this.

Now as I said (ab)^2 is the same as a^{2}b^{2}

So to simplify the numerator, (2 \times x^{\frac{1}{2}})^{4} \Rightarrow (2)^{4}(x^{\frac{1}{2}})^{4}

Can you work from here? \frac{(2)^{4}(x^{\frac{1}{2}})^{  4}}{8x}
so I did 2 to the power of 4 which is 16 and x ^1/2 times the power of 4 to get

16(x)^2over 8x

then I simplified to get only 2^2 which is 4 and then on my calculator i substituted the 4 for x and got 8 as my answer

is this correct?
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ManLike007
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(Original post by Anonymous1502)
so I did 2 to the power of 4 which is 16 and x ^1/2 times the power of 4 to get

16(x)^2over 8x
So you have \frac{16x^{2}}{8x} which is correct.


(Original post by Anonymous1502)
then I simplified to get only 2^2 which is 4 and then on my calculator i substituted the 4 for x and got 8 as my answer
I don't quite understand what you've done here because your answer should be in the form of ax where a is an integer, I don't know what you've substituted in unless you haven't told the full question.

Let me simplify this a bit more for you,

\frac{16x^{2}}{8x} is the same as \frac{16}{8} \times \frac{x^{2}}{x}

Can you work from here?
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Anonymous1502
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(Original post by ManLike007)
So you have \frac{16x^{2}}{8x} which is correct.




I don't quite understand what you've done here because your answer should be in the form of ax where a is an integer, I don't know what you've substituted in unless you haven't told the full question.

Let me simplify this a bit more for you,

\frac{16x^{2}}{8x} is the same as \frac{16}{8} \times \frac{x^{2}}{x}

Can you work from here?
16/8 simplifies to 2. x^2/x simplifies to only x, so 2 * x =2x. So is 2x the correct answer or do I have to do another step?
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ManLike007
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(Original post by Anonymous1502)
16/8 simplifies to 2. x^2/x simplifies to only x, so 2 * x =2x. So is 2x the correct answer or do I have to do another step?
Yes that's correct! The answer simplifies down to 2x. You're just simplifying as your original post said.
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Anonymous1502
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(Original post by ManLike007)
Yes that's correct! The answer simplifies down to 2x. You're just simplifying as your original post said.
Thank you,Im not very capable at maths, so your help has been really useful.
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