Trigonometry Examples

$8^{x} = 32768$

Step 1

Create equivalent expressions in the equation that all have equal bases.

$2^{3 x} = 2^{15}$

Step 2

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$3 x = 15$

Step 3

Divide each term in $3 x = 15$ by $3$ and simplify.

Tap for more steps...

Step 3.1

Divide each term in $3 x = 15$ by $3$ .

$\frac{3 x}{3} = \frac{15}{3}$

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 3.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{15}{3}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{15}{3}$

Step 3.3

Simplify the right side.

Tap for more steps...

Step 3.3.1

Divide $15$ by $3$ .

$x = 5$