Question

If logY X is Z, then what is the value of the log of

X^-3 to the base of Y^-1?​

Answer 1

SOLUTION

GIVEN

$\displaystyle \sf{ log_{Y}(X) = Z }$

TO DETERMINE

$\displaystyle \sf{ log_{{Y }^{ - 1} }({X}^{ - 3} ) }$

EVALUATION

Here it is given that

$\displaystyle \sf{ log_{Y}(X)= Z }$

$\displaystyle \sf{ \implies \: \frac{log_{}(X)}{log(Y)} = Z }$

Now

$\displaystyle \sf{ log_{{Y }^{ - 1} }({X}^{ - 3} ) }$

$\displaystyle \sf{ = \frac{log_{}({X}^{ - 3} )}{log({Y}^{ - 1} )} }$

$\displaystyle \sf{ = \frac{ - 3 \times log_{}({X}^{ } )}{ - 1 \times log({Y}^{ } )} }$

$\displaystyle \sf{ =3 \times \frac{ log_{}({X}^{ } )}{ log({Y}^{ } )} }$

$\displaystyle \sf{ = 3 \times log_{Y}(X) }$

$\displaystyle \sf{ = 3 \times Z }$

$\displaystyle \sf{ = 3Z }$

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