Question

Hi, I was absent today in class and I really need help with question 5 I will be much appreciated if you show work and the step so I can be more understanding thank you!

Answer 1

We will have the folowing:

$x^{3.2}=87$

First, we take 3.2 to it's fraction form, that is:

$3.2=\frac{16}{5}$

So:

$x^{\frac{16}{5}}=87\Rightarrow\ln (x^{\frac{16}{5}})=\ln (87)$$\Rightarrow\frac{16}{5}\ln (x)=\ln (87)\Rightarrow\ln (x)=\frac{5\ln (87)}{16}$$\Rightarrow e^{\ln (x)}=e^{(\frac{5\ln(87)}{16})}\Rightarrow x=e^{(\ln (87^{\frac{5}{16}})}$$\Rightarrow x=87^{\frac{5}{16}}$