Trigonometry Examples

$93 = 4^{3 x}$

Step 1

Rewrite the equation as $4^{3 x} = 93$ .

$4^{3 x} = 93$

Step 2

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

$\ln (4^{3 x}) = \ln (93)$

Step 3

Expand $\ln (4^{3 x})$ by moving $3 x$ outside the logarithm.

$3 x \ln (4) = \ln (93)$

Step 4

Divide each term in $3 x \ln (4) = \ln (93)$ by $3 \ln (4)$ and simplify.

Tap for more steps...

Step 4.1

Divide each term in $3 x \ln (4) = \ln (93)$ by $3 \ln (4)$ .

$\frac{3 x \ln (4)}{3 \ln (4)} = \frac{\ln (93)}{3 \ln (4)}$

Step 4.2

Simplify the left side.

Tap for more steps...

Step 4.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 4.2.1.1

Cancel the common factor.

$\frac{3 x \ln (4)}{3 \ln (4)} = \frac{\ln (93)}{3 \ln (4)}$

Step 4.2.1.2

Rewrite the expression.

$\frac{x \ln (4)}{\ln (4)} = \frac{\ln (93)}{3 \ln (4)}$

Step 4.2.2

Cancel the common factor of $\ln (4)$ .

Tap for more steps...

Step 4.2.2.1

Cancel the common factor.

$\frac{x \ln (4)}{\ln (4)} = \frac{\ln (93)}{3 \ln (4)}$

Step 4.2.2.2

Divide $x$ by $1$ .

$x = \frac{\ln (93)}{3 \ln (4)}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\ln (93)}{3 \ln (4)}$

Decimal Form:

$x = 1.08985980 \dots$