Solve for x 8*2^(3x)=1

$8 \cdot 2^{3 x} = 1$

Simplify.

Rewrite $8$ as $2^{3}$ .

$2^{3} \cdot 2^{3 x} = 1$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2^{3 + 3 x} = 1$

Divide each term in $2^{3 + 3 x} = 1$ by $8$ .

$\frac{2^{3 + 3 x}}{8} = \frac{1}{8}$

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$2^{3 + 3 x} = 1$

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

$\ln (2^{3 + 3 x}) = \ln (1)$

Expand $\ln (2^{3 + 3 x})$ by moving $3 + 3 x$ outside the logarithm.

$(3 + 3 x) \ln (2) = \ln (1)$

Simplify the left side.

Apply the distributive property.

$3 \ln (2) + 3 x \ln (2) = \ln (1)$

Simplify the right side.

The natural logarithm of $1$ is $0$ .

$3 \ln (2) + 3 x \ln (2) = 0$

Reorder $3 \ln (2)$ and $3 x \ln (2)$ .

$3 x \ln (2) + 3 \ln (2) = 0$

Subtract $3 \ln (2)$ from both sides of the equation.

$3 x \ln (2) = - 3 \ln (2)$

Divide each term in $3 x \ln (2) = - 3 \ln (2)$ by $3 \ln (2)$ and simplify.

Divide each term in $3 x \ln (2) = - 3 \ln (2)$ by $3 \ln (2)$ .

$\frac{3 x \ln (2)}{3 \ln (2)} = \frac{- 3 \ln (2)}{3 \ln (2)}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x \ln (2)}{3 \ln (2)} = \frac{- 3 \ln (2)}{3 \ln (2)}$

Rewrite the expression.

$\frac{x \ln (2)}{\ln (2)} = \frac{- 3 \ln (2)}{3 \ln (2)}$

Cancel the common factor of $\ln (2)$ .

Cancel the common factor.

$\frac{x \ln (2)}{\ln (2)} = \frac{- 3 \ln (2)}{3 \ln (2)}$

Divide $x$ by $1$ .

$x = \frac{- 3 \ln (2)}{3 \ln (2)}$

Simplify the right side.

Cancel the common factor of $- 3$ and $3$ .

Factor $3$ out of $- 3 \ln (2)$ .

$x = \frac{3 (- \ln (2))}{3 \ln (2)}$

Cancel the common factors.

Factor $3$ out of $3 \ln (2)$ .

$x = \frac{3 (- \ln (2))}{3 \ln (2)}$

Cancel the common factor.

$x = \frac{3 (- \ln (2))}{3 \ln (2)}$

Rewrite the expression.

$x = \frac{- \ln (2)}{\ln (2)}$

Cancel the common factor of $\ln (2)$ .

Cancel the common factor.

$x = \frac{- \ln (2)}{\ln (2)}$

Divide $- 1$ by $1$ .

$x = - 1$

Solve for x 8*2^(3x)=1

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