QuestionFind $\log_{b} B^{2}$ if $\log_{b} A = 5$ and $\log_{b} B = -4$ .

Studdy Solution

STEP 1

Assumptions1. $\log{b} A=5$ . $\log{b} B=-4$

STEP 2

We need to find the value of $\log{b} B^{2}$ . We know that $\log{b} B=-4$ , so we can use the property of logarithms that states $\log{b} x^{n}=n \log{b} x$ .
$\log{b} B^{2} =2 \log{b} B$

STEP 3

Substitute the value of $\log{b} B$ into the equation.
$\log{b} B^{2} =2 \times (-)$

STEP 4

Calculate the value of the expression.
$\log{b} B^{2} = -8$ So, the value of $\log{b} B^{2}$ is -8.

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