Question

Solve the exponential equation using logarithmic properties y=3^2x-4

The 2x is an exponent

Answer 1

`(log(y+4))/(2log3)`

Explanation:

Given the exponential equation
`y = 3^(2x)+4`, to get 2x, we will make 2x the subject of the formula as shown;

`y = 3^(2x)-4\\y+4 = 3^(2x)\\taking\ log\ of\ both\ sides\\log(y+4) = log3^(2x)\\ log(y+4) = 2xlog3\\dividing\ both\ sides\ by\ 2log 3\\\ x = (log(y-4))/(2log3) \\`

The last expression gives the required value of x