Question

3^x=2 5^y=3 and 2^z=5 value of xyz

Answer 1

Answer:

1

Explanation:

solving for x, we introduce ln on both sides

$ln(3^{x})=ln2\\x*ln3=ln2\\x=\frac{ln2}{ln3}$

solving for y;

$ln(5^{y} )=ln3\\y*ln5=ln3\\y=\frac{ln3}{ln5}$

solving for z;

$ln(2^{z})=ln5\\z*ln2=ln5\\z=\frac{ln5}{ln2}$

Now;

$x*y*z=\frac{ln2}{ln3}*\frac{ln3}{ln5} *\frac{ln5}{ln2}  \\x*y*z=1$