Question

if 3^x = 5^y = 45^z prove that x = 2yz/( y_z).​

Answer 1

Answer:

Step-by-step explanation:

$3^{x} = 5^{y} = 45^{z} = k\\3^{x} = k\\\\3 = \sqrt[x]{k} \\3= k^{1/x}\\\\5 = \sqrt[y]{k} \\5= k^{1/y}\\\\\\45 = \sqrt[z]{k} \\45 = k^{1/z}\\\\45 = 5 * 3^{2} \\k^{1/z} = k^{1/y} * k^{2/x}\\k^{1/z} = k^{1/y + 2/x}\\\frac{1}{z}=\frac{1}{y}+\frac{2}{x} \\\frac{1}{z}-\frac{1}{y} =\frac{2}{x}\\\frac{y - z}{yz} = \frac{2}{x}\\x = \frac{2yz}{y-z}$