Question

Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original log expression. Give exact answer.
log4x=log5+log(x-2)

my work so far:
log4x=log5(x-2)
log4x=log5x-10

Answer 1

Since these are \[\log_{10} \]

Use this property on both sides of your equation.\[10^{\log_{10}x}=x\]So the left side will be:\[10^{\log_{10}4x }=4x\]The right side will be:\[10^{\log_{10}(5x-10) }=5x-10\]