Answer to Question #178239 in Algebra for Festus

Question

Convert y = 2 (16/9)^3x to base 16/9

Answer 1

Given, the function $y=2(16/9)^{3x}$ .

Divide by 2 both side.

$y=2(16/9)^{3x} \newline \frac{y}{2}=(\frac{16}{9})^{3x}$

Apply logarithm both side.

$log(\frac{y}{2})=3xlog(\frac{16}{9})$

Divide by $log(\frac{16}{9})$ both side.

$\frac{log(\frac{y}{2})}{log(\frac{16}{9})}=3x$

From logarithm property, $log_{b} a=\frac{log_{e}a}{log_{e}b}$.

Then, $log_{\frac{16}{9}}\frac{y}{2}=3x$.

Thus, the required answer is $log_{\frac{16}{9}}\frac{y}{2}=3x$.