Solve for x log base 49 of 1/7=x

$\log_{49} (\frac{1}{7}) = x$

Step 1

Rewrite the equation as $x = \log_{49} (\frac{1}{7})$ .

$x = \log_{49} (\frac{1}{7})$

Step 2

Logarithm base $49$ of $\frac{1}{7}$ is $- \frac{1}{2}$ .

Rewrite as an equation.

$x = \log_{49} (\frac{1}{7}) = x$

Rewrite $\log_{49} (\frac{1}{7}) = x$ 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 $b^{y} = x$ .

$x = 49^{x} = \frac{1}{7}$

Create expressions in the equation that all have equal bases.

$x = {(7^{2})}^{x} = 7^{- 1}$

Rewrite ${(7^{2})}^{x}$ as $7^{2 x}$ .

$x = 7^{2 x} = 7^{- 1}$

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

$x = 2 x = - 1$

Solve for $x$ .

$x = x = - \frac{1}{2}$

The variable $x$ is equal to $- \frac{1}{2}$ .

$x = - \frac{1}{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{1}{2}$

Decimal Form:

$x = - 0.5$

Solve for x log base 49 of 1/7=x

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