Solve for x 34x15x1SolutionSolution 34x15x1 Taking log of bo

Solve for x

3^(4x+1)=5^(x+1)

Solution:

3^(4x+1)=5^(x+1)

Taking log of both side we get

(4x+1) log3 = (x+1) log 5 ....( since log a^b = b log a )

or (4x+1) log3 = (x+1) log 5

or 4x log 3 + log 3 = x log 5+log 5

or 4x log 3 -x log 5 = log 5 - log 3

or x( 4log 3-log 5) = log5 - log3

Thus x = (log5 - log3) /( 4log 3-log 5)

x = log(5/3) / ( log3^4 -log 5)

x = log(5/3) / log (81/ 5)

Hence x = 0.1834196 Ans