Solve for x 24* log of 3x=60

$24 \cdot \log (3 x) = 60$

Divide each term in $(24 \cdot \log (3 x)) = 60$ by $24$ and simplify.

Divide each term in $(24 \cdot \log (3 x)) = 60$ by $24$ .

$\frac{(24 \cdot \log (3 x))}{24} = \frac{60}{24}$

Simplify the left side.

Cancel the common factor of $24$ .

Cancel the common factor.

$\frac{24 \cdot \log (3 x)}{24} = \frac{60}{24}$

Divide $\log (3 x)$ by $1$ .

$\log (3 x) = \frac{60}{24}$

Simplify the right side.

Cancel the common factor of $60$ and $24$ .

Factor $12$ out of $60$ .

$\log (3 x) = \frac{12 (5)}{24}$

Cancel the common factors.

Factor $12$ out of $24$ .

$\log (3 x) = \frac{12 \cdot 5}{12 \cdot 2}$

Cancel the common factor.

$\log (3 x) = \frac{12 \cdot 5}{12 \cdot 2}$

Rewrite the expression.

$\log (3 x) = \frac{5}{2}$

Rewrite $\log (3 x) = \frac{5}{2}$ 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 $b^{y} = x$ .

$10^{\frac{5}{2}} = 3 x$

Solve for $x$ .

Rewrite the equation as $3 x = 10^{\frac{5}{2}}$ .

$3 x = 10^{\frac{5}{2}}$

Divide each term in $3 x = 10^{\frac{5}{2}}$ by $3$ and simplify.

Divide each term in $3 x = 10^{\frac{5}{2}}$ by $3$ .

$\frac{3 x}{3} = \frac{10^{\frac{5}{2}}}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{10^{\frac{5}{2}}}{3}$

Divide $x$ by $1$ .

$x = \frac{10^{\frac{5}{2}}}{3}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{10^{\frac{5}{2}}}{3}$

Decimal Form:

$x = 105.40925533 \dots$

Solve for x 24* log of 3x=60

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