Algebra Examples

$\log_{4} (m - 3) = \frac{1}{2}$

Step 1

Rewrite $\log_{4} (m - 3) = \frac{1}{2}$ 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 $b^{y} = x$ .

$4^{\frac{1}{2}} = m - 3$

Step 2

Solve for $m$ .

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Step 2.1

Rewrite the equation as $m - 3 = 4^{\frac{1}{2}}$ .

$m - 3 = 4^{\frac{1}{2}}$

Step 2.2

Simplify $4^{\frac{1}{2}}$ .

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Step 2.2.1

Rewrite.

$m - 3 = 0 + 0 + 4^{\frac{1}{2}}$

Step 2.2.2

Simplify the expression.

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Step 2.2.2.1

Rewrite $4$ as $2^{2}$ .

$m - 3 = {(2^{2})}^{\frac{1}{2}}$

Step 2.2.2.2

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

$m - 3 = 2^{2 (\frac{1}{2})}$

Step 2.2.3

Cancel the common factor of $2$ .

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Step 2.2.3.1

Cancel the common factor.

$m - 3 = 2^{2 (\frac{1}{2})}$

Step 2.2.3.2

Rewrite the expression.

$m - 3 = 2^{1}$

Step 2.2.4

Evaluate the exponent.

$m - 3 = 2$

Step 2.3

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

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Step 2.3.1

Add $3$ to both sides of the equation.

$m = 2 + 3$

Step 2.3.2

Add $2$ and $3$ .

$m = 5$