Solve for x : 3^(2x-1)=5^(x+1)

The equation 3^(2x-1)=5^(x+1) has to be solved for
x.

It is only possible to solve the given equation by the
use of logarithm and an approximate result can be
obtained.

Take the log to base 10 of both the sides of the
equation.

log(3^(2x-1))=log(5^(x+1))

Use
the property of logarithm log a^b = b*log a

(2x - 1)*log 3
= (x + 1)*log 5

(2x - 1)/(x + 1) = log 5/log
3

Now the value of log 5/log 3 is approximately
1.464973521

2x - 1 = (x
+1)*1.464973521

x*(2 - 1.464973521) = 1.464973521 +
1

x*0.5350364793 =
2.464973521

x =
2.464973521/0.5350364793

x =
4.60711300325

The solution of the equation is x =
4.60711300325