Maths A level Help-Indices and Logarithims Watch

tom3232
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Hi,

I am quite stuck on these two questions and am not quite sure how to approach them. If you could do a step by step answer or go through a similar question then it would be much appreciated.

Thank You

Questions:


Solve this equation

25^x=5^x+1 -6


and

Find the values of x for which

Log3 (x) - 2logx (3)=1
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TenOfThem
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(Original post by tom3232)
Hi,

I am quite stuck on these two questions and am not quite sure how to approach them. If you could do a step by step answer or go through a similar question then it would be much appreciated.

Thank You

Questions:


Solve this equation

25^x=5^x+1 -6


and

Find the values of x for which

Log3 (x) - 2logx (3)=1

Do you not have step by step examples in your text book or your class notes?
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tom3232
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(Original post by TenOfThem)
Do you not have step by step examples in your text book or your class notes?
No, which is why I am at such an impasse.

Any help would be great
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Notnek
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(Original post by tom3232)
No, which is why I am at such an impasse.

Any help would be great
25^x = (5^2)^x = (5^x)^2
5^(x+1) = 5(5^x)

Rewriting the equation:

(5^x)^2 = 5(5^x) - 6

Can you continue from here?


For the second one, use the change of base formula:

\displaystyle \log_a b = \frac{\log_c b}{\log_c a}
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tom3232
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(Original post by notnek)
25^x = (5^2)^x = (5^x)^2
5^(x+1) = 5(5^x)

Rewriting the equation:

(5^x)^2 = 5(5^x) - 6

Can you continue from here?


For the second one, use the change of base formula:

\displaystyle \log_a b = \frac{\log_c b}{\log_c a}



Thanks for the reply.

Can you explain how you got to

25^x = (5^2)^x = (5^x)^2

We were taught that you could 25^x=5^2x

So I am a bit confused.
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TenOfThem
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(Original post by tom3232)
Thanks for the reply.

Can you explain how you got to

25^x = (5^2)^x = (5^x)^2

We were taught that you could 25^x=5^2x

So I am a bit confused.
I assume that you know that 2x = x2 so that 5^{2x} = (5^2)^x = (5^x)^2
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Notnek
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(Original post by tom3232)
Thanks for the reply.

Can you explain how you got to

25^x = (5^2)^x = (5^x)^2

We were taught that you could 25^x=5^2x

So I am a bit confused.
It's also equal to 5^(2x).

25^x = (5^2)^x = 5^(2x) = (5^x)^2

In general (a^b)^c = (a^c)^b
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tom3232
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Ok Thanks.

Could you explain how you 5^x+1 to be 5(5x)?

Thank You
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Notnek
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(Original post by tom3232)
Ok Thanks.

Could you explain how you 5^x+1 to be 5(5x)?

Thank You
5^x \times 5^1 = 5^{x+1}
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