How do I solve an exponential equation with numbers^x on each side?

I think I am really blanking out.


The problem is: 3 times 11^x = 7 times 2^x





Thanks for the help!How do I solve an exponential equation with numbers^x on each side?
Here's a big hint:


11^x / 7^x = (11/7) ^ x


That's how you combine the two x's into a single x.


How do I solve an exponential equation with numbers^x on each side?
3(11)^x = 7(2)^x





7 /3 = (11 /7)^x





taking logs





ln(7 / 3) = x ln(11 / 7)





x = ln (7 / 3) / ln(11 / 7)





x = 1.875
3*11^x = 7*2^x





Taking the ln of each side:





ln(3) + x*ln(11) = ln(7)+x*ln(2)





collecting terms and transposing:





x*[ln(11)-ln(2)] = ln(7) - ln(3)





x = [ln(7) - ln(3)]/[ln(11) - ln(2)]





x = .49702