SOLUTION: log[4](x)+log[8](x)=1

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Question 373206: log[4](x)+log[8](x)=1
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
log%284%2C%28x%29%29%2Blog%288%2C%28x%29%29=1
y1%2By2=1
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.
.
y1=log%284%2C%28x%29%29
4%5Ey1=x
%282%5E2%29%5Ey1=x
2%5E%282%2Ay1%29=x
.
.
y2=log%288%2C%28x%29%29
8%5Ey2=x
%282%5E3%29%5Ey2=x
2%5E%283%2Ay2%29=x
.
.
.
2%5E%282%2Ay1%29=2%5E%283%2Ay2%29
2y1=3%2Ay2%29
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.
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Substitute,
y1%2By2=1
2y1%2B2y2=2
3y2%2B2y2=2
5y2=2
y2=2%2F5
y1=3%2F5
.
.
x=4%5E%28y1%29=8%5E%28y2%29
highlight%28x=root%285%2C4%5E%283%29%29=root%285%2C8%5E%282%29%29%29 or approximately,
x=2.2974