Question

3(2^x) = 6^2x
How do you solve this?

Answer 1

`3(2^x)=6^(2x)`

`3(2^x)=(3*2)^(2x)`

`3(2^x)=3^(2x)2^(2x)`

`\ln(3(2^x))=\ln(3^(2x)2^(2x))`

`\ln3+\ln2^x=\ln3^(2x)+\ln2^(2x)`

`\ln3+x\ln2=2x\ln3+2x\ln2`

`\ln3=2x\ln3+2x\ln2-x\ln2`

`\ln3=x(2\ln3+\ln2)`

`x=(\ln3)/(2\ln3+\ln2)`