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Popular >

simplify ln(x^5)-2ln(sqrt(x))

Solution

simplify

ln (x^{5}) - 2 ln (x)

Solution

ln (x^{4})

Solution steps

ln (x^{5}) - 2 ln (x)

Apply log rule:

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

2 ln (x) = ln ((x)^{2})

= ln (x^{5}) - ln ((x)^{2})

Apply log rule:

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

ln (x^{5}) - ln ((x)^{2}) = ln (\frac{x ^{5}}{( x ) ^{2}})

= ln (\frac{x ^{5}}{( x ) ^{2}})

Simplify

\frac{x ^{5}}{( x ) ^{2}} : x^{4}

= ln (x^{4})

Popular Examples

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simplify log_{5}(k^2-25)-log_{5}(k-5)simplify

lo g_{5} (k^{2} - 25) - lo g_{5} (k - 5)

expand log_{10}((sqrt(y)z^4)/x)expand

lo g_{10} (\frac{y z ^{4}}{x})

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lo g_{10} (\frac{x ^{2} y ^{3}}{y z ^{2}})

simplify ln(25(0^2+1)^2)simplify

ln (25 (0^{2} + 1)^{2})

Frequently Asked Questions (FAQ)

What is ln(x^5)-2ln(sqrt(x)) ?
The solution to ln(x^5)-2ln(sqrt(x)) is ln(x^4)