logarithms?

Question

Please help me find the solve this step by step:
Expand the log in terms of +,-,/, and *.

a) log(10xsqrt(x-3))

b) ln (x^2 sin^3 x)/(sqrt x^2 + 1)

Thanks

Answer 1

Start with the basics log(xy) = log(x) + log(y) also
log( sqrt(x)) = 1/2 * log( x) or simply log( x^n) = n*log(x)

now for a) log(10xsqrt(x-3)) = log(10) + log(x) + log(sqrt(x-3)) = 1 + log(x) + 1/2*log(x-3) I assume that log(10) = 1 if the log is base 10 log.

b) ln( x^2 sin^3 x)/(sqrt x^2 + 1) = (2*ln(x) + 3 * ln(sin(x))) /( sqrt(x^2) + 1)

I don't know what other form you may be looking for.