Question

Write the expression as a single logarithm.

4log₆x-1/5 log₆z + 2log₆y

Answer 1

$\frac{4log_{6}(x-1)}{5log_{6}z+2log_{6}y}$

$=>\frac{log_{6}(x-1)⁴}{log_{6}z⁵+log_{6}y²}$

$=>\frac{log_{6}(x-1)⁴}{log_{6}z⁵y²}$

Recall that $\frac{log_{x} a}{log_{x}b} = log_{b}a$

$=>\frac{log_{6}(x-1)⁴}{log_{6}z⁵y²}={log_{z⁵y}(x-1)⁴}$