Basic Math Examples

200000 = 20^{a}

$200000 = 20^{a}$

Step 1

Rewrite the equation as

20^{a} = 200000

$20^{a} = 200000$ .

20^{a} = 200000

$20^{a} = 200000$

Step 2

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

\ln (20^{a}) = \ln (200000)

$\ln (20^{a}) = \ln (200000)$

Step 3

Expand

\ln (20^{a})

$\ln (20^{a})$ by moving

a

$a$ outside the logarithm.

a \ln (20) = \ln (200000)

$a \ln (20) = \ln (200000)$

Step 4

Divide each term in

a \ln (20) = \ln (200000)

$a \ln (20) = \ln (200000)$ by

\ln (20)

$\ln (20)$ and simplify.

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Step 4.1

Divide each term in

a \ln (20) = \ln (200000)

$a \ln (20) = \ln (200000)$ by

\ln (20)

$\ln (20)$ .

\frac{a \ln (20)}{\ln (20)} = \frac{\ln (200000)}{\ln (20)}

$\frac{a \ln (20)}{\ln (20)} = \frac{\ln (200000)}{\ln (20)}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of

\ln (20)

$\ln (20)$ .

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Step 4.2.1.1

Cancel the common factor.

\frac{a \ln (20)}{\ln (20)} = \frac{\ln (200000)}{\ln (20)}

$\frac{a \ln (20)}{\ln (20)} = \frac{\ln (200000)}{\ln (20)}$

Step 4.2.1.2

Divide

a

$a$ by

1

$1$ .

a = \frac{\ln (200000)}{\ln (20)}