Algebra Examples

2^{x} = 100

$2^{x} = 100$

Step 1

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

\ln (2^{x}) = \ln (100)

$\ln (2^{x}) = \ln (100)$

Step 2

Expand

\ln (2^{x})

$\ln (2^{x})$ by moving

x

$x$ outside the logarithm.

x \ln (2) = \ln (100)

$x \ln (2) = \ln (100)$

Step 3

Divide each term in

x \ln (2) = \ln (100)

$x \ln (2) = \ln (100)$ by

\ln (2)

$\ln (2)$ and simplify.

Tap for more steps...

Step 3.1

Divide each term in

x \ln (2) = \ln (100)

$x \ln (2) = \ln (100)$ by

\ln (2)

$\ln (2)$ .

\frac{x \ln (2)}{\ln (2)} = \frac{\ln (100)}{\ln (2)}

$\frac{x \ln (2)}{\ln (2)} = \frac{\ln (100)}{\ln (2)}$

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Cancel the common factor of

\ln (2)

$\ln (2)$ .

Tap for more steps...

Step 3.2.1.1

Cancel the common factor.

\frac{x \ln (2)}{\ln (2)} = \frac{\ln (100)}{\ln (2)}

$\frac{x \ln (2)}{\ln (2)} = \frac{\ln (100)}{\ln (2)}$

Step 3.2.1.2

Divide

x

$x$ by

1

$1$ .

x = \frac{\ln (100)}{\ln (2)}