Precalculus Examples

$7 \log_{4} (0.6 x) = 12$

Step 1

Divide each term in $7 \log_{4} (0.6 x) = 12$ by $7$ and simplify.

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Step 1.1

Divide each term in $7 \log_{4} (0.6 x) = 12$ by $7$ .

$\frac{7 \log_{4} (0.6 x)}{7} = \frac{12}{7}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $7$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{7 \log_{4} (0.6 x)}{7} = \frac{12}{7}$

Step 1.2.1.2

Divide $\log_{4} (0.6 x)$ by $1$ .

$\log_{4} (0.6 x) = \frac{12}{7}$

Step 2

Rewrite $\log_{4} (0.6 x) = \frac{12}{7}$ 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 $b^{y} = x$ .

$4^{\frac{12}{7}} = 0.6 x$

Step 3

Solve for $x$ .

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Step 3.1

Rewrite the equation as $0.6 x = 4^{\frac{12}{7}}$ .

$0.6 x = 4^{\frac{12}{7}}$

Step 3.2

Divide each term in $0.6 x = 4^{\frac{12}{7}}$ by $0.6$ and simplify.

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Step 3.2.1

Divide each term in $0.6 x = 4^{\frac{12}{7}}$ by $0.6$ .

$\frac{0.6 x}{0.6} = \frac{4^{\frac{12}{7}}}{0.6}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $0.6$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{0.6 x}{0.6} = \frac{4^{\frac{12}{7}}}{0.6}$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{4^{\frac{12}{7}}}{0.6}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $12$ by $7$ .

$x = \frac{4^{1.\overline{714285}}}{0.6}$

Step 3.2.3.2

Raise $4$ to the power of $1.\overline{714285}$ .

$x = \frac{10.76720154}{0.6}$

Step 3.2.3.3

Divide $10.76720154$ by $0.6$ .

$x = 17.9453359$