Precalculus Examples

$\frac{\ln (6)}{6 \ln (6) + \ln (5)}$

Step 1

Simplify $6 \ln (6)$ by moving $6$ inside the logarithm.

$\frac{\ln (6)}{\ln (6^{6}) + \ln (5)}$

Step 2

Raise $6$ to the power of $6$ .

$\frac{\ln (6)}{\ln (46656) + \ln (5)}$

Step 3

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\frac{\ln (6)}{\ln (46656 \cdot 5)}$

Step 4

Multiply $46656$ by $5$ .

$\frac{\ln (6)}{\ln (233280)}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{\ln (6)}{\ln (233280)}$

Decimal Form:

$0.14496442 \dots$