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Popular >

expand ln((5a)/(bc))

Solution

expand

ln (\frac{5 a}{b c})

Solution

ln (5) + ln (a) - ln (b) - ln (c)

Solution steps

ln (\frac{5 a}{b c})

Apply log rule:

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

ln (\frac{5 a}{b c}) = ln (5 a) - ln (b c)

= ln (5 a) - ln (b c)

Apply log rule:

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

ln (5 a) = ln (5) + ln (a), ln (b c) = ln (b) + ln (c)

= ln (5) + ln (a) - (ln (b) + ln (c))

- (ln (b) + ln (c)) : - ln (b) - ln (c)

= ln (5) + ln (a) - ln (b) - ln (c)

Popular Examples

simplify-log_{10}(6.2*10^{-5})simplify

- lo g_{10} (6.2 \cdot 1 0^{- 5})

simplify 0.0259*ln((4*10^{12})/(1.5*10^{10)})simplify

0.0259 \cdot ln (\frac{4 \cdot 1 0 ^{12}}{1.5 \cdot 1 0 ^{10}})

simplify ln(32/5)simplify

ln (\frac{32}{5})

simplify log_{10}(4x^3)-1/2 log_{10}((x+3)(x-2))simplify

lo g_{10} (4 x^{3}) - \frac{1}{2} lo g_{10} ((x + 3) (x - 2))

expand log_{2}((xyz)^3)expand

lo g_{2} ((x yz)^{3})

Frequently Asked Questions (FAQ)

What is expand ln((5a)/(bc)) ?
The solution to expand ln((5a)/(bc)) is ln(5)+ln(a)-ln(b)-ln(c)