Question

Solve for x(explicitly and to 4 decimal places):
e^(3x-2)=32
Explain also please?

Answer 1

\[e^{(3x-2)}=32\][taking log both sides]
\[\log e^{(3x-2)}=\log 32 \rightarrow (3x-2) \log e=\log 32\]
\[ \rightarrow (3x-2) \times 1=\log 32 ---(\log e = 1)\]
\[(3x-2) =\log 32 \rightarrow 3x-2 =1.5051 \rightarrow 3x =2+1.5051\]
\[ \rightarrow 3x =3.5051 \rightarrow x = \frac{3.5051}{3}=1.1683\]
Hence x =1.1683 is the required answer.

@bwoods130