Evaluate log base 2 of 6+ log base 3 of 5

$\log_{2} (6) + \log_{3} (5)$

Step 1

Rewrite $\log_{2} (6)$ using the change of base formula.

The change of base rule can be used if $a$ and $b$ are greater than $0$ and not equal to $1$ , and $x$ is greater than $0$ .

$\log_{a} (x) = \frac{\log_{b} (x)}{\log_{b} (a)} + \log_{3} (5)$

Substitute in values for the variables in the change of base formula, using $b = 10$ .

$\frac{\log (6)}{\log (2)} + \log_{3} (5)$

Step 2

Rewrite $\log_{3} (5)$ using the change of base formula.

The change of base rule can be used if $a$ and $b$ are greater than $0$ and not equal to $1$ , and $x$ is greater than $0$ .

$\frac{\log (6)}{\log (2)} + \log_{a} (x) = \frac{\log_{b} (x)}{\log_{b} (a)}$

Substitute in values for the variables in the change of base formula, using $b = 10$ .

$\frac{\log (6)}{\log (2)} + \frac{\log (5)}{\log (3)}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{\log (6)}{\log (2)} + \frac{\log (5)}{\log (3)}$

Decimal Form:

$4.04993602 \dots$