# Maths question- A level help please

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#1
Hey,

a) Solve the equation: x^2-10x+9=0

Which I got x=9 and x=1

b) Hence, or otherwise, solve the equation

3^x-2(3^x -10)=-1

I'm struggling with part b.

Thanks,
V 0
1 month ago
#2
Expand and use a suitable substitution for 3^x
1
1 month ago
#3
(Original post by Voss.gloss20)
Hey,

a) Solve the equation: x^2-10x+9=0

Which I got x=9 and x=1

b) Hence, or otherwise, solve the equation

3^x-2(3^x -10)=-1

I'm struggling with part b.

Thanks,
V Make a substitution so that this equation becomes 1
#4
Thank you. How would I know in the future to out y=3x rather than y=3x-2 for example?
0
1 month ago
#5
(Original post by Voss.gloss20)
Thank you. How would I know in the future to out y=3x rather than y=3x-2 for example?
The sub y=3^x is the most natural and gives the part a) equation directly. So it would be the one to try first so the word "hence" in the question.

y=3^(x-2)=3^x/9 would give
y(9y-10)=-1
or
9y^2 - 10y + 1 = 0
which is similar, and gives the same result in the end (for x=...), but its less obvious how to use the part a, so the "or otherwise" in the question.
0
#6
(Original post by mqb2766)
The sub y=3^x is the most natural and gives the part a) equation directly. So it would be the one to try first so the word "hence" in the question.

y=3^(x-2)=3^x/9 would give
y(9y-10)=-1
or
9y^2 - 10y + 1 = 0
which is similar, and gives the same result in the end (for x=...), but its less obvious how to use the part a, so the "or otherwise" in the question.
Ohh right. Thanks 1
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