Question

Write the expression as a as a single logarithm 5log2+log3=

Answer 1

Given the expression;

`5\log_(2+\log_(3`

Following addition and power property of logarithm;

`\begin{gathered} a\log_b=\log_b^a \\ \\ \log_a+\log_b=\log_ab \end{gathered}`

Thus;

`\begin{gathered} 5\log_(10)2+\log_(10)3=\log_(10)2^5+\log_(10)3 \\ \\ 5\log_(10)2+\log_(10)3=\log_(10)32+\log_(10)3 \\ \\ 5\log_(10)2+\log_(10)3=\log_(10)(32*3) \\ \\ 5\log_(10)2+\log_(10)3=\log_(10)96 \end{gathered}`

ANSWER:

`\log_(10)96`