Question

How do I solve this?

Answer 1

`\large\boxed{x=\log_(5)/(3)5}`

Explanation:

`3^x=5^(x-1)\qquad\text{use}\ a^(n-m)=(a^n)/(a^m)\\\\3^x=(5^x)/(5^1)\qquad\text{multiply both sides by 5}\\\\5\cdot3^x=5^x\qquad\text{divide both sides by}\ 3^x\\\\5=(5^x)/(3^x)\qquad\text{use}\ \left((a)/(b)\right)^n=(a^n)/(b^n)\\\\5=\left((5)/(3)\right)^x\qquad\text{logarithm both sides}\ \log_(5)/(3)\\\\\log_(5)/(3)5=\log_(5)/(3)\left((5)/(3)\right)^x\qquad\text{use}\ \log_ab^n=n\log_ab\\\\\log_(5)/(3)5=x\log_(5)/(3)(5)/(3)\qquad\text{use}\ \log_aa=1\\\\\log_(5)/(3)5=x`