SOLUTION: Question: Solve and round to the nearest hundredth. 7^x+2-4=136.

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Question 201513: Question: Solve and round to the nearest hundredth. 7^x+2-4=136.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
I assume the problem is to solve: 7%5E%28x%2B2%29+-+4+=+136

To start with, add 4 to both sides giving
7%5E%28x%2B2%29+=+140
Next, since 140 is not a power of 7 (it is a multiple but not a power), we will need to use logarithms. Use base 10 logarithms or natural logarithms, it doesn't matter. I will use base 10:
log%28%287%5E%28x%2B2%29%29%29+=+log%28%28140%29%29
The log%28140%29 is approximately 2.146128 so now we have
log%28%287%5E%28x%2B2%29%29%29+=+2.146128
Using a property of logarithms (log%28%28a%5Eb%29%29+=+b%2Alog%28%28a%29%29) we get
%28x%2B2%29%2Alog%28%287%29%29+=+2.146128
Dividing by log(7) we get
x%2B2+=+2.146128%2F%28log%28%287%29%29%29
The log(7) is approximately 0.845098 giving us
x+%2B+2+=+2.146128%2F0.845098+=+2.539501
Subtracting 2 from both sides we get (rounded to the nearest hundredth):
x = 0.56