Precalculus Examples

5 \log_{5} (7)

$5 \log_{5} (7)$

Step 1

Simplify

5 \log_{5} (7)

$5 \log_{5} (7)$ by moving

5

$5$ inside the logarithm.

\log_{5} (7^{5})

$\log_{5} (7^{5})$

Step 2

Raise

7

$7$ to the power of

5

$5$ .

\log_{5} (16807)

$\log_{5} (16807)$

Step 3

Rewrite

\log_{5} (16807)

$\log_{5} (16807)$ using the change of base formula.

Tap for more steps...

Step 3.1

The change of base rule can be used if

a

$a$ and

b

$b$ are greater than

0

$0$ and not equal to

1

$1$ , and

x

$x$ is greater than

0

$0$ .

\log_{a} (x) = \frac{\log_{b} (x)}{\log_{b} (a)}

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

Step 3.2

Substitute in values for the variables in the change of base formula, using

b = 10

$b = 10$ .

\frac{\log (16807)}{\log (5)}

$\frac{\log (16807)}{\log (5)}$

\frac{\log (16807)}{\log (5)}

$\frac{\log (16807)}{\log (5)}$

Step 4

The result can be shown in multiple forms.

Exact Form:

\frac{\log (16807)}{\log (5)}

$\frac{\log (16807)}{\log (5)}$

Decimal Form:

6.04530977 \dots

$6.04530977 \dots$

5 \log_{5} (7)

$5 \log_{5} (7)$

(

)

[

]

√



≥

















≤

















∞















