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Popular >

simplify ln(x^6)-2ln(sqrt(x^5))

Solution

simplify

ln (x^{6}) - 2 ln (x^{5})

Solution

ln (x)

Solution steps

ln (x^{6}) - 2 ln (x^{5})

Apply log rule:

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

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

= ln (x^{6}) - ln ((x^{5})^{2})

Apply log rule:

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

ln (x^{6}) - ln ((x^{5})^{2}) = ln \frac{x ^{6}}{( x ^{5} ) ^{2}}

= ln \frac{x ^{6}}{( x ^{5} ) ^{2}}

Simplify

\frac{x ^{6}}{( x ^{5} ) ^{2}} : x

= ln (x)

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Frequently Asked Questions (FAQ)

What is ln(x^6)-2ln(sqrt(x^5)) ?
The solution to ln(x^6)-2ln(sqrt(x^5)) is ln(x)