(3^x)(4^2x+1)=(6^x+2). Find the exact value of x giving the answer in the form x=ln(a)/ln(b).

Answer 1

Use your log rules
(3^x)(4^2x+1)=(6^x+2)
log[(3^x)(4^2x+1)]= log(6^x+2)
xlog3 + (2x+1)log4 = (x+2)log6
xlog3 + x(2log4) + log4 = xlog6 + 2log4
x(log3 + 2log4 - log6) = 2log4 - log4
x(log8) = log9
x = log9/log8

Answer 2

Thank you so much! I got to the third step and then couldn't figure out how to go about it without using decimals..but thanks so much!