Question 27c70

Jan 22, 2017

x≈4.090" to 3 dec. places"

Explanation:

Isolate the exponential by dividing both sides by 40

$\Rightarrow {\left(1.5\right)}^{x} = \frac{210}{40} = \frac{21}{4}$

$\textcolor{\mathmr{and} a n \ge}{\text{Reminder }} \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{\log {x}^{n} = n \log x} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

Take the ln ( natural log) of both sides.

$\Rightarrow \ln {\left(1.5\right)}^{x} = \ln \left(\frac{21}{4}\right)$

$\Rightarrow x \ln \left(1.5\right) = \ln \left(\frac{21}{4}\right)$

rArrx=(ln(21/4))/(ln1.5)≈4.090" to 3 dec.places"#