Question

Solve the exponential equation using logarithmic properties y=3^2x-4The 2x is an exponent

Answer 1

Answer:

$\frac{log(y+4)}{2log3}$

Step-by-step explanation:

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

$y = 3^{2x}-4\\y+4 = 3^{2x}\\taking\ log\ of\ both\ sides\\log(y+4) = log3^{2x}\\ log(y+4) = 2xlog3\\dividing\ both\ sides\ by\ 2log 3\\\ x = \frac{log(y-4)}{2log3}$

The last expression gives the required value of x