Finite Math Examples

$7^{3} = 8^{p}$

Step 1

Rewrite the equation as $8^{p} = 7^{3}$ .

$8^{p} = 7^{3}$

Step 2

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

$\ln (8^{p}) = \ln (7^{3})$

Step 3

Expand $\ln (8^{p})$ by moving $p$ outside the logarithm.

$p \ln (8) = \ln (7^{3})$

Step 4

Simplify the right side.

Tap for more steps...

Step 4.1

Raise $7$ to the power of $3$ .

$p \ln (8) = \ln (343)$

Step 5

Divide each term in $p \ln (8) = \ln (343)$ by $\ln (8)$ and simplify.

Tap for more steps...

Step 5.1

Divide each term in $p \ln (8) = \ln (343)$ by $\ln (8)$ .

$\frac{p \ln (8)}{\ln (8)} = \frac{\ln (343)}{\ln (8)}$

Step 5.2

Simplify the left side.

Tap for more steps...

Step 5.2.1

Cancel the common factor of $\ln (8)$ .

Tap for more steps...

Step 5.2.1.1

Cancel the common factor.

$\frac{p \ln (8)}{\ln (8)} = \frac{\ln (343)}{\ln (8)}$

Step 5.2.1.2

Divide $p$ by $1$ .

$p = \frac{\ln (343)}{\ln (8)}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$p = \frac{\ln (343)}{\ln (8)}$

Decimal Form:

$p = 2.80735492 \dots$