Question

College Algebra

Suppose three variables x, a, and b exist such that:

logx (a) = 2
logx (b) = -3

Evaluate the expression given below:

logx (ab^2)=

logx (a^2/b^3)=

Answer 1

`log_(x)(a {b}^(2) ) =`

`log_(x)(a) + log_(x)( {b}^(2) ) =`

`log_(x)(a) + 2 log_(x)(b) =`

`2 + 2( - 3) = 2 + ( - 6) = - 4`

`log_(x)( \frac{ {a}^(2) }{ {b}^(3) } ) =`

`log_(x)( {a}^(2) ) - log_(x)( {b}^(3) ) =`

`2 log_(x)(a) - 3 log_(x)(b) =`

`2(2) - 3( - 3) = 4 + 9 = 13`