How do you solve 3(5^(x-1))=21?

2 Answers

x=\frac{\ln35}{\ln5}

Explanation:

Given that

3(5^{x-1})=21

5^{x-1}=21/3

5^{x-1}=7

Taking logs on both the sides as follows

\ln5^{x-1}=\ln 7

(x-1)\ln 5=\ln7

x-1=\frac{\ln 7}{\ln 5}

x=\frac{\ln 7}{\ln 5}+1

x=\frac{\ln 7+\ln 5}{\ln 5}

x=\frac{\ln35}{\ln5}

Jul 27, 2018

x=2.21 (2.d.p)

Explanation:

3(5^(x-1))=21

5^(x-1)=7

log_10 5^(x-1)=log_10 7

(x-1) log_10 5=log_10 7

x-1=log_10 7/log_10 5

x=1+log_10 7/log_10 5

x=2.21 (2.d.p)