Logarithmic Problem 2^x+1=5^2x-3?
Was on my midterm today and I am not sure how to do it.
I will show my work:
2^x+1=5^2x-3
2^x+1=25^x-3
(x+1)log2=(x-3)log25
xlog2+log2=xlog25-3log25
xlog2-xlog25=-log2-3log25
x(log2-log25)=-log2-3log25
x=(-log2-3log25)/(log2-log25)
x=4.098
But when I did my check and plugged x back in, it did not check out right... Any help?
Update:Oh.. Don't know why I was under the impression that you could do that... Thanks
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Verified answer
Your method is fine but you missed a bit in the very beginning
5^(2x-3) ≠ 25^(x-3)
The error you made is in the first step.
5^(2x-3) does not equal 25^(x-3).
You would have to factor out a 2 from the 2x and from the 3 for this to work.
Instead, you should have gone straight to logarithms:
(x+1)log2 = (2x-3)log5
log2 x + log2 = 2log5 x - 3log5
log2 x - 2log5 x = -log2 - 3log5
(log2 - 2log5) x = -log2 - 3log5
x = (-log2 - 3log5) / (log2 - 2log5)
x = 2.186 (approx)
Hope this helps.