Question

Use the properties of logarithms to write the following expression as a single term that doesn't contain a logarithm.e6-8ln(x)+In(y)

Answer 1

Given:

The expression is,

$e^{6-8\ln (x)+\ln (y)}$

Explanation:

Simplify the expression by using logathimic properties.

$\begin{gathered} e^{6-8\ln (x)+\ln (y)_{}}=e^{6-\ln (x^8)+\ln (y)} \\ =e^6\cdot e^{-\ln (x^8)}\cdot e^{\ln (y)} \end{gathered}$

Simplify further.

$\begin{gathered} e^6\cdot e^{-\ln (x^8)}\cdot e^{\ln (y)}=e^6\cdot\frac{1}{e^{\ln(x^8)}}\cdot e^{\ln (y)} \\ =e^6\cdot\frac{1}{x^8}\cdot y \\ =\frac{e^6y}{x^8} \end{gathered}$

So answer is,

$\frac{e^6y}{x^8}$