Solve for x log base 4 of 3x=6

$\log_{4} (3 x) = 6$

Step 1

Rewrite $\log_{4} (3 x) = 6$ 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 $b^{y} = x$ .

$4^{6} = 3 x$

Step 2

Solve for $x$ .

Rewrite the equation as $3 x = 4^{6}$ .

$3 x = 4^{6}$

Divide each term in $3 x = 4^{6}$ by $3$ and simplify.

Divide each term in $3 x = 4^{6}$ by $3$ .

$\frac{3 x}{3} = \frac{4^{6}}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{4^{6}}{3}$

Divide $x$ by $1$ .

$x = \frac{4^{6}}{3}$

Simplify the right side.

Raise $4$ to the power of $6$ .

$x = \frac{4096}{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{4096}{3}$

Decimal Form:

$x = 1365.\overline{3}$

Mixed Number Form:

$x = 1365 \frac{1}{3}$

Solve for x log base 4 of 3x=6

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