Hey can you help me find the exact value of x in the equation 5^2x=3^(x+1)? Thanks a lot, this website is cool and helpful!

Answer 1

take the log of both sides

log(5^2x) = log (3^(x+1))
2xlog5 = (x+1)log3
2xlog5 = xlog3 + log3
2xlog5 - xlog3 = log3
x(2log5 - log3) = log 3
x = log3/(2log5 - log3)
x = .5181489...