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Popular >

simplify 7ln(a)-4ln(b)

Solution

simplify

7 \cdot ln (a) - 4 \cdot ln (b)

Solution

ln (\frac{a ^{7}}{b ^{4}})

Solution steps

7 ln (a) - 4 ln (b)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

7 ln (a) = ln (a^{7})

= ln (a^{7}) - 4 ln (b)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

4 ln (b) = ln (b^{4})

= ln (a^{7}) - ln (b^{4})

Apply log rule:

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

ln (a^{7}) - ln (b^{4}) = ln (\frac{a ^{7}}{b ^{4}})

= ln (\frac{a ^{7}}{b ^{4}})

Popular Examples

simplify log_{b}(x+1)-log_{b}(x)simplify

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lo g_{10} (x) + lo g_{10} (x + 5)

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lo g_{10} (x) + lo g_{10} (x + 1)

simplify ln(x/(sqrt(x^2+7)))simplify

ln (\frac{x}{x ^{2} + 7})

Frequently Asked Questions (FAQ)

What is 7*ln(a)-4*ln(b) ?
The solution to 7*ln(a)-4*ln(b) is ln((a^7)/(b^4))