Question

If (64)^x = (48)^y = (36)^z show that 1/x + 1/z = 2/y​

Answer 1

Answer:

$let \: {64}^{x} = {48}^{y} = {36}^{z} = k \\ so \\ 64 = {k}^{ \frac{1}{x} } \\ 48 = {k}^{ \frac{1}{y} } \\ 36 = {k}^{ \frac{1}{z} } \\ now \\ 64 \times 36 = {48}^{2} \\ or \\ {k}^{ \frac{1}{x} } \times {k}^{ \frac{1}{z} } = {( {k}^{ \frac{1}{y} } )}^{2} \\ {k}^{ \frac{1}{x} + \frac{1}{z} } = {k}^{ \frac{2}{y} } \\ or \\ \frac{1}{x} + \frac{1}{z} = \frac{2}{y}$