Question

log(x^9 + 8)
to base e
i need full steps

Answer 1

the change of base formula when converting from base a to base b is\[\log_{a} x=\frac{\log_{b}x}{\log_{b}a} \]

Answer 2

In your case you have a common log (base 10) that you want to change to base e (natural log) so relative to the formula a=10 and b=e:\[\log(x^9+8)=\frac{\ln (x^9+8)}{\ln 10}\]note that ln is a shorthand notation for "log to the base e"

Answer 3

\[\log_e x=\ln x\]