SOLUTION: Help!!! Solve the following equation s: a) 9 log5 base x =log x base 5 B) log x/2 base 8 = log x base 2

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Question 1087750: Help!!! Solve the following equation s:
a) 9 log5 base x =log x base 5
B) log x/2 base 8 = log x base 2
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

a)
9log%285+%2C+x%29+=log+%285%2Cx%29
log%285+%2C+x%5E9%29+=log+%285%2Cx%29 since log and base same
x%5E9+=x
x%5Ecross%289%29%5E8+=cross%28x%291
x%5E8+=1
=>x=1
B)
log+%288%2Cx%2F2+%29+=+log+%282%2Cx+%29 ...in base 10 will be
+log+%28x%2F2+%29+%2F+log+%288+%29=+log+%28x+%29+%2F+log+%282%29
log+%28x%2F2+%29+%2F+log+%282%5E3+%29=+log+%28x+%29+%2F+log+%282%29
log+%28x%2F2+%29+%2F+3log+%282%29=+log+%28x+%29+%2F+log+%282%29
log+%28x%2F2+%29+=3log+%282%29%28+log+%28x+%29+%2F+log+%282%29%29
log+%28x%2F2+%29+=3cross%28log+%282%29%29%28+log+%28x+%29+%2F+cross%28log+%282%29%29%29
log+%28x%2F2+%29+=3+log+%28x+%29
+log+%28x%2F2+%29+=+log+%28x%5E3+%29+ if so, than
x%2F2++=+x%5E3+
x+=+2x%5E3+
cross%28x%291+=+2x%5Ecross%283%29%5E2+
1+=+2x%5E2+
x%5E2=1%2F2
x+=+1%2Fsqrt%282%29