# How do you solve 2^x=4.5?

Jul 22, 2016

$x = \frac{\ln 4.5}{\ln 2} \approx 2.17$

#### Explanation:

Take logs of both sides:

$\ln {2}^{x} = \ln 4.5$

Using power rule of logs, bring the x down in front

$x \ln 2 = \ln 4.5$

Rearrange:

$x = \frac{\ln 4.5}{\ln 2}$

$x = \log \frac{9}{\log} 2 - 1 = 2.16992500144$

#### Explanation:

Given ${2}^{x} = 4.5$, Find $x$

Solution:

${2}^{x} = 4.5$

Take the logarithm of both sides of the equation

$\log {2}^{x} = \log \frac{9}{2}$

$x \cdot \log 2 = \log 9 - \log 2$

divide both sides of the equation by $\log 2$

$\frac{x \cdot \log 2}{\log} 2 = \frac{\log 9 - \log 2}{\log} 2$

$\frac{x \cdot \cancel{\log} 2}{\cancel{\log}} 2 = \frac{\log 9 - \log 2}{\log} 2$

$x = \log \frac{9}{\log} 2 - 1$

$x = 2.16992500144$

God bless....I hope the explanation is useful.