Question

Guys help me do this...plzz we have online tests tomorrow please guys..help me ​

Answer 1

Question :

The value of $\bf\: 3 {}^{ - 2 log_{3}(5) }$ is

Logarithm properties:

$1) log(a) + log(b) = log(ab)$

$2) log( \frac{a}{b} ) = log(a) - log(b)$

$3) log(a) {}^{n} = n log(a)$

$4) log_{x}(x) = 1$

Solution :

we have to find the value of $3 {}^{ - 2 log_{3}(5) }$

$\bf 3 {}^{ - 2 log_{3}(5) }$

we know that $n log(a)=log(a){}^{n}$

$= \sf 3 {}^{ log_{3}(5 {}^{ - 2} ) }$

use property $\sf\:\log_{x}(x) = 1$

$= 5 {}^{ - 2}$

$= \frac{1}{5 {}^{2} }$

$= \frac{1}{25}$

Therefore ;

${\purple{\boxed{\large{\bold{\bf\:3{}^{-2 log_{3}(5)}=\dfrac{1}{25}}}}}}$

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More About Logarithm :

The Logarithm function is defined as

$f(x) = log_{b}(x)$

where b > 0 and b ≠ 1 and also x >0, reads as log base b of x.