SOLUTION: what is the solution to 3^(2x)=125?

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Question 932172: what is the solution to 3^(2x)=125?
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

3%5E%282x%29=125
3%5E%282x%29=5%5E3...use log
log%283%5E%282x%29%29=log%285%5E3%29
%282x%29log%283%29=3log%285%29
x=%283%2F2%29log%285%29%2Flog%283%29
x=%283%2F2%29log%285%29%2Flog%283%29 ...in base 10, log%285%29=0.69897 and log%283%29=0.4771212547 approximately (because exact value is to long)
x=%281.5%29%280.69897%2F0.4771212547%29
x=%281.5%29%281.464973512%29
x=2.197460268
x=2.197460268
check:
3%5E%282%2A2.197460268%29=124.999996, rounded to whole number it is 125

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

what is the solution to 3^(2x)=125?


3%5E%282x%29+=+125

log+%283%2C+125%29+=+2x -------- Logarithmic form

2x+=+%28log+125%29%2Flog+3%29+=+2x

x+=+%28log+125%2Flog+3%29%2F2, or x+=+4.394920562%2F2, or highlight_green%28x+=+%0D%0A2.197460281%29