Question

Condense the logarithmic expression:4 log2 y + 1/3 log2 x^3

Answer 1

Given:

`4\log _2y+(1)/(3)\log _2x^3`
`\log a^b=b\log a`

Then:

`\begin{gathered} 4\log _2y+(1)/(3)\log _2x^3 \\ =\log _2y^4+\log _2(x^3)^{(1)/(3)} \\ =\log _2y^4+\log _2x \end{gathered}`
`\log ab=\log a+\log b`
`\begin{gathered} =\log _2y^4+\log _2x \\ =\log _2(y^4x) \end{gathered}`