Solve for x log base 64 of 16=x

$\log_{64} (16) = x$

Step 1

Rewrite the equation as $x = \log_{64} (16)$ .

$x = \log_{64} (16)$

Step 2

Logarithm base $64$ of $16$ is $\frac{2}{3}$ .

Rewrite as an equation.

$x = \log_{64} (16) = x$

Rewrite $\log_{64} (16) = x$ in exponential form using the definition of a logarithm. If $x$ and $b$ are positive real numbers and $b$ does not equal $1$ , then $\log_{b} (x) = y$ is equivalent to $b^{y} = x$ .

$x = 64^{x} = 16$

Create expressions in the equation that all have equal bases.

$x = {(2^{6})}^{x} = 2^{4}$

Rewrite ${(2^{6})}^{x}$ as $2^{6 x}$ .

$x = 2^{6 x} = 2^{4}$

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

$x = 6 x = 4$

Solve for $x$ .

$x = x = \frac{2}{3}$

The variable $x$ is equal to $\frac{2}{3}$ .

Factor $2$ out of $4$ .

$x = \frac{2 (2)}{6}$

Cancel the common factors.

Factor $2$ out of $6$ .

$x = \frac{2 \cdot 2}{2 \cdot 3}$

Cancel the common factor.

$x = \frac{2 \cdot 2}{2 \cdot 3}$

Rewrite the expression.

$x = \frac{2}{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{2}{3}$

Decimal Form:

$x = 0.\overline{6}$

Solve for x log base 64 of 16=x

Related Questions

Support LCMGCF.com by disabling your adblocker.