Question

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

Answer 1

Given:

$4\log _2y+\frac{1}{3}\log _2x^3$$\log a^b=b\log a$

Then:

$\begin{gathered} 4\log _2y+\frac{1}{3}\log _2x^3 \\ =\log _2y^4+\log _2(x^3)^{\frac{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}$