# How do you solve 2*20^n=18?

Sep 19, 2016

≈ 0.733

#### Explanation:

Using the $\textcolor{b l u e}{\text{law of logarithms}}$

$\textcolor{\mathmr{and} a n \ge}{\text{Reminder }} \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{\ln {x}^{n} = n \ln x} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

The first step here is to divide both sides by 2.

$\Rightarrow {20}^{n} = 9$

To obtain n as a multiplier rather than as an index, take ln of both sides.

$\Rightarrow \ln {20}^{n} = \ln 9$

$\Rightarrow n \ln 20 = \ln 9$

rArrn=(ln9)/(ln20)≈0.733" to 3 decimal places"

Sep 19, 2016

#### Answer:

$n = 0.73345$

#### Explanation:

$2 \times {20}^{n} = 18 \text{ } \leftarrow \div 2$

${20}^{n} = 9$

9 is clearly not a power of 20, so logs are indicated.

$\log {20}^{n} = \log 9$

$n \log 20 = \log 9$

$n = \log \frac{9}{\log} 20$

$n = 0.73345$