Solve for x log base (x+3) of 8=1/2

$\log_{(x + 3)} (8) = \frac{1}{2}$

Step 1

Rewrite $\log_{x + 3} (8) = \frac{1}{2}$ in exponential form using the definition of a logarithm. If $x$ and $b$ are positive real numbers and $b \neq 1$ , then $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ .

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

Step 2

Solve for $x$ .

Raise each side of the equation to the power of $2$ to eliminate the fractional exponent on the left side.

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

Simplify the exponent.

Simplify the left side.

Simplify ${({(x + 3)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(x + 3)}^{\frac{1}{2}})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

${(x + 3)}^{1} = 8^{2}$

Simplify.

$x + 3 = 8^{2}$

Simplify the right side.

Raise $8$ to the power of $2$ .

$x + 3 = 64$

Move all terms not containing $x$ to the right side of the equation.

Subtract $3$ from both sides of the equation.

$x = 64 - 3$

Subtract $3$ from $64$ .

$x = 61$

Solve for x log base (x+3) of 8=1/2

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