SOLUTION: having difficulty solving the following equation. can you help? 10^x+3 = 6^2x

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Question 418423: having difficulty solving the following equation. can you help?
10^x+3 = 6^2x

Found 2 solutions by ankor@dixie-net.com, solver91311:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Assume the problem is:
10%5E%28x%2B3%29+=+6%5E%282x%29
using common logs we have
log%2810%5E%28x%2B3%29%29+=+log%286%5E%282x%29%29
log equiv of exponents
%28x%2B3%29log%2810%29+=+2x%2Alog%286%29
we know the log of 10 = 1, therefore
x + 3 = 2x*.778
x + 3 = 1.556x
3 = 1.556x - x
3 =.556x
x = 3%2F.556
x = 5.393
:
:
Check this on your calc: enter 10^8.393 and 6^10.786, should be close to the same value

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Presuming you mean:



Mainly because



can only be solved by numerical methods,

take the base 10 log of both sides:



Use the laws of logarithms:





(Because )

The rest is elementary algebra:



John

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