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Popular >

simplify ln((40^2)/(10^2))

Solution

simplify

ln (\frac{4 0 ^{2}}{1 0 ^{2}})

Solution

2 ln (40) - 2 ln (10)

+1

Decimal Notation

2.77258 \dots

Solution steps

ln (\frac{4 0 ^{2}}{1 0 ^{2}})

Apply log rule:

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

ln (\frac{4 0 ^{2}}{1 0 ^{2}}) = ln (4 0^{2}) - ln (1 0^{2})

= ln (4 0^{2}) - ln (1 0^{2})

Apply log rule:

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

ln (4 0^{2}) = 2 ln (40)

= 2 ln (40) - ln (1 0^{2})

Apply log rule:

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

ln (1 0^{2}) = 2 ln (10)

= 2 ln (40) - 2 ln (10)

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Frequently Asked Questions (FAQ)

What is ln((40^2)/(10^2)) ?
The solution to ln((40^2)/(10^2)) is 2ln(40)-2ln(10)