solve the equation!!!!!!!!!!!!!!!!!!!!!!!

Question

3(2^(x-3))=6^(x-1)

Answer 1

3(2^(x-3))=6^(x-1)

Using basic exponent rule

a^(m-n)=a^m/a^n

3(2^(x-3))=6^(x-1)

3(2^x/2^3)=6^x/6^1

3*2^x/8=6^x/6

3*2^x/4=(2*3)^x/3

(9/4)2^x=(2*3)^x

Using basic exponent rule

(ab)^m=a^m*b*m

(9/4)2^x=2^x*3^x

Cancel common terms

(9/4)=3^x

xln3=ln(9/4)

x=ln(9/4)/ln3

   =ln  (9/4)

        3