How do you solve 5^x = 3^(x+2)?

1 Answer
Mar 5, 2018

x~~4.301color(white)(88) 3.d.p.

Explanation:

5^x=3^(x+2)

Taking logarithms of both sides:

By the law of logarithms:

lna^b=bln(a)

xln(5)=(x+2)ln(3)

xln(5)=xln(3)+2ln(3)

Subtract xln(3) from both sides:

xln(5)-xln(3)=2ln(3)

Factor LHS

x(ln(5)-ln(3))=2ln(3)

Divide by (ln(5)-ln(3))

x=(2ln(3))/(ln(5)-ln(3))

x~~4.301color(white)(88) 3.d.p.