Algebra Examples

10^{x} = 5

$10^{x} = 5$

Step 1

Take the base

10

$10$ logarithm of both sides of the equation to remove the variable from the exponent.

\log (10^{x}) = \log (5)

$\log (10^{x}) = \log (5)$

Step 2

Expand the left side.

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Step 2.1

Expand

\log (10^{x})

$\log (10^{x})$ by moving

x

$x$ outside the logarithm.

x \log (10) = \log (5)

$x \log (10) = \log (5)$

Step 2.2

Logarithm base

10

$10$ of

10

$10$ is

1

$1$ .

x \cdot 1 = \log (5)

$x \cdot 1 = \log (5)$

Step 2.3

Multiply

x

$x$ by

1

$1$ .

x = \log (5)

$x = \log (5)$

x = \log (5)

$x = \log (5)$

Step 3

The result can be shown in multiple forms.

Exact Form:

x = \log (5)

$x = \log (5)$

Decimal Form:

x = 0.69897000 \dots

$x = 0.69897000 \dots$

10^{x} = 5

$10^{x} = 5$

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