SOLUTION: Solve: y=log base 2 (2x) and y=log base 4 (x).

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Question 1111151: Solve: y=log base 2 (2x) and y=log base 4 (x).
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

y=log+%282+%2C2x%29
+y=log++%284%2Cx%29
left sides are equal, then
log+%282+%2C2x%29+=log++%284%2Cx%29
log+%282x%29%2Flog%282%29+=log++%28x%29%2Flog%284%29
log%282x%29%2Alog%284%29+=log%28x%29%2Alog%282%29
log%282x%29%2Alog%282%5E2%29+=log%28x%29%2Alog%282%29
log%282x%29%2A2log%282%29+=log%28x%29%2Alog%282%29
2log%282x%29+=log%28x%29
log+%284x%5E2%29+=log%28x%29
4x%5E2=x
4x%5E2%2Fx=x%2Fx
4x=1
x=1%2F4
plug in x in any given equation above and find y
y=log+%282+%2C2x%29
y=log+%282+%2C2%281%2F4%29%29+
y=log+%282+%2C1%2F2%29+
y=+-1