What is log_{3}(1/(25*3*5^{53)}) ?

The solution to log_{3}(1/(25*3*5^{53)}) is -(55log_{3}(5)+1)

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simplify log_{3}(1/(2535^{53)})

simplify

lo g_{3} (\frac{1}{25 \cdot 3 \cdot 5 ^{53}})

- (55 lo g_{3} (5) + 1)

Decimal Notation

- 81.57354 \dots

Solution steps

lo g_{3} (\frac{1}{25 \cdot 3 \cdot 5 ^{53}})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

lo g_{3} (\frac{1}{25 \cdot 3 \cdot 5 ^{53}}) = lo g_{3} (1) - lo g_{3} (25 \cdot 3 \cdot 5^{53})

= lo g_{3} (1) - lo g_{3} (5^{53} \cdot 25 \cdot 3)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

lo g_{3} (25 \cdot 3 \cdot 5^{53}) = lo g_{3} (25) + lo g_{3} (3) + lo g_{3} (5^{53})

= lo g_{3} (1) - (lo g_{3} (3) + lo g_{3} (25) + lo g_{3} (5^{53}))

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{3} (5^{53}) = 53 lo g_{3} (5)

= lo g_{3} (1) - (lo g_{3} (25) + lo g_{3} (3) + 53 lo g_{3} (5))

lo g_{3} (1) = 0

- (lo g_{3} (25) + lo g_{3} (3) + 53 lo g_{3} (5)) = - (55 lo g_{3} (5) + 1)

= 0 - (55 lo g_{3} (5) + 1)

0 - (55 lo g_{3} (5) + 1) = - (55 lo g_{3} (5) + 1)

= - (55 lo g_{3} (5) + 1)

ln (ln (y)) + ln (x)

lo g_{y} (2 e^{5}) - lo g_{y} (5 e^{8})

\frac{3}{4} (ln (7) - ln (5))

ln (\frac{y ^{2}}{2 y})

lo g_{\frac{1}{2} (\frac{3}{5}),} (x)

What is log_{3}(1/(25*3*5^{53)}) ?
The solution to log_{3}(1/(25*3*5^{53)}) is -(55log_{3}(5)+1)