Question

logarithms class 11th​

Answer 1

Given :   $x^{\log \frac{y}{z}}.y^{\log \frac{z}{x}}.z^{\log \frac{x}{y}}.$

To Find : Value of expression

log x

log y

log z

1

Solution:

Let say given expression is  = A

$x^{\log \frac{y}{z}}.y^{\log \frac{z}{x}}.z^{\log \frac{x}{y}}.$ = A

taking log both sides

and using

log mn  = logm + logn

and log  aⁿ  = n loga

=>  log (y/z) log x  + log (z /x) log y  + log ( x/y) log z = log A

using log (m/n) = log m - log n

=>( log y - log z) logx + (logz - log x) log y  + (log x - log y) logz = log A

=>  0  = log A

=> A = 1

Hence expression = 1

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