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Popular >

simplify ln(50)*ln(1/50)

Solution

simplify

ln (50) \cdot ln (\frac{1}{50})

Solution

- ln^{2} (50)

+1

Decimal Notation

- 15.30392 \dots

Solution steps

ln (50) ln (\frac{1}{50})

Apply log rule:

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

ln (\frac{1}{50}) = ln (1) - ln (50)

= ln (50) (ln (1) - ln (50))

Apply log rule:

lo g_{a} (1) = 0

= ln (50) (- ln (50) + 0)

0 - ln (50) = - ln (50)

= ln (50) (- ln (50))

Remove parentheses:

(- a) = - a

= - ln (50) ln (50)

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

ln (50) ln (50) = ln^{1 + 1} (50)

= - ln^{1 + 1} (50)

Add the numbers:

1 + 1 = 2

= - ln^{2} (50)

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Frequently Asked Questions (FAQ)

What is ln(50)*ln(1/50) ?
The solution to ln(50)*ln(1/50) is -ln^2(50)