Question

If $a^x=b^y=c^z=abc$, then $\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=$__

• A. -1
• B. xyz
• C. 1
• D. $\frac{1}{xyz}$

Answer 1

The correct option is C 1

$a^x=b^y=c^z=abc$

$a^x=abc\Rightarrow a=(abc{)}^{1/x}$ ___ (1)

$b^y=abc\Rightarrow b=(abc{)}^{1/y}$ ___ (2)

$c^z=abc\Rightarrow c=(abc{)}^{1/z}$ ___ (3)

Multiply (1), (2), (3)

$\Rightarrow abc=\left(abc\right)(\frac{1}{x}+\frac{1}{y}+\frac{1}{z})$

$\Rightarrow \frac{1}{x}+\frac{1}{y}+\frac{1}{z}=1$

(Comparing coff.)