SOLUTION: 3^(2x-1) = 5^(x+4) ^ = to the power of

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Question 926367: 3^(2x-1) = 5^(x+4)
^ = to the power of
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-1%29+=+5%5E%28x%2B4%29

3%5E%282x%29%2F3+=+5%5E%28x%2B4%29
%283%5E2%29%5Ex%29=+3%2A5%5E%28x%2B4%29

9%5Ex=+3%2A5%5E%28x%2B4%29.....use logarithm
log%289%5Ex%29=+log%283%2A5%5E%28x%2B4%29%29
x%2Alog%289%29=+log%283%2A5%5E%28x%2B4%29%29
x=+log%283%2A5%5E%28x%2B4%29%29%2Flog%289%29
x=+%28log%283%29%2Blog%285%5E%28x%2B4%29%29%29%2Flog%283%5E2%29
x=+%28log%283%29%2B%28x%2B4%29%28log%285%29%2F2log%283%29%29%29
x=+log%283%29%2F2log%283%29%2B%28x%2B4%29%28log%285%29%2F2log%283%29%29
x=+1%2F2+%2B%28x%2B4%29%28log%285%29%2F2log%283%29%29
x+=1%2F2%2B%28x%2B4%29%28log%285%29%2F2log%283%29%29........0.732486760358963583598520203839320198153966183333024844526445=log%285%29%2F2log%283%29 or round it to 0.73248676+=log%285%29%2F2log%283%29

x=1%2F2%2B0.73248676%28x%2B4%29

x=0.5%2B0.73248676x%2B2.92994704

x-0.73248676x=0.5%2B2.92994704

%281-0.73248676%29x=0.5%2B2.92994704

%280.26751324%29x=3.42994704

x=3.42994704%2F0.26751324

x=12.8216

check:
3%5E%282x-1%29+=+5%5E%28x%2B4%29
3%5E%2825.6432-1%29+=+5%5E%2812.8216%2B4%29
3%5E%2824.6432%29+=+5%5E%2816.8216%29
5.72525+%2A10%5E11=5.72524%2A+10%5E11
5.73%2A10%5E11=5.73%2A10%5E11



Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
3^(2x-1) = 5^(x+4)
^ = to the power of
3%5E%282x+-+1%29+=+5%5E%28x+%2B+4%29

log+3%5E%282x+-+1%29+=+log+5%5E%28x+%2B+4%29 ------- Taking logs of both sides

%282x+-+1%29+log+3+=+%28x+%2B+4%29+log+5

%282x+-+1%29%2F%28x+%2B+4%29+=+log+5%2Flog+3

%282x+-+1%29%2F%28x+%2B+4%29+=+1.464974

2x+-+1+=+1.464974%28x+%2B+4%29 ----- Cross-multiplying

              2x – 1 = 1.464974x + 5.85989

2x – 1.464974x = 5.85989 + 1

         .535026x = 6.85989

                    x+=+6.85989%2F.535026, or highlight_green%2812.8216%29

You can do the check!! 

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