QuestionFind $\log_{b} \frac{A}{B}$ given $\log_{b} A=2$ and $\log_{b} B=-4$ .

Studdy Solution

STEP 1

Assumptions1. $\log{b} A=$ . $\log{b} B=-4$
3. We are looking for the value of $\log{b} \frac{A}{B}$

STEP 2

We can use the property of logarithms that states $\log{b} \frac{A}{B} = \log{b} A - \log{b} B$ .
$\log{b} \frac{A}{B} = \log{b} A - \log{b} B$

STEP 3

Now, we can substitute the given values of $\log{b} A$ and $\log{b} B$ into the equation.
$\log{b} \frac{A}{B} =2 - (-)$

STEP 4

Calculate the value of $\log{b} \frac{A}{B}$ .
$\log{b} \frac{A}{B} =2 - (-4) =6$ So, the value of $\log{b} \frac{A}{B}$ is6.

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