Algebra Examples

$3 \log (x) - \log (6) + \log (2.4) = 9$

Step 1

Simplify the left side.

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Step 1.1

Log base $10$ of $2.4$ is approximately $0.38021124$ .

$3 \log (x) - \log (6) + 0.38021124 = 9$

Step 1.2

Add $- \log (6)$ and $0.38021124$ .

$3 \log (x) - 0.39794 = 9$

Step 2

Move all terms not containing $\log (x)$ to the right side of the equation.

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Step 2.1

Add $0.39794$ to both sides of the equation.

$3 \log (x) = 9 + 0.39794$

Step 2.2

Add $9$ and $0.39794$ .

$3 \log (x) = 9.39794$

Step 3

Divide each term in $3 \log (x) = 9.39794$ by $3$ and simplify.

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Step 3.1

Divide each term in $3 \log (x) = 9.39794$ by $3$ .

$\frac{3 \log (x)}{3} = \frac{9.39794}{3}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $3$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{3 \log (x)}{3} = \frac{9.39794}{3}$

Step 3.2.1.2

Divide $\log (x)$ by $1$ .

$\log (x) = \frac{9.39794}{3}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $9.39794$ by $3$ .

$\log (x) = 3.13264666$

Step 4

Rewrite $\log (x) = 3.13264666$ 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 $b^{y} = x$ .

$10^{3.13264666} = x$

Step 5

Solve for $x$ .

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Step 5.1

Rewrite the equation as $x = 10^{3.13264666}$ .

$x = 10^{3.13264666}$

Step 5.2

Raise $10$ to the power of $3.13264666$ .

$x = 1357.20880829$