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skeeter

MHF Helper
Jun 2008
16,216
6,764
North Texas
solve for x
log4(5-2x)=3

log5(8x)-log5(3)=log5(x+10)
\(\displaystyle \log_4(5-2x) = 3\)

change to an exponential equation ...

\(\displaystyle 4^3 = 5-2x\)

finish


\(\displaystyle \log_5(8x)-\log_5(3)=\log_5(x+10)\)

combine logs on the left using the log difference property ...

\(\displaystyle \log_5\left(\frac{8x}{3}\right) = \log_5(x+10)\)

\(\displaystyle \frac{8x}{3} = x+10\)

finish