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Popular >

simplify 2ln(6x)-2/3 ln(x^3)

Solution

simplify

2 ln (6 x) - \frac{2}{3} ln (x^{3})

Solution

2 ln (6)

+1

Decimal Notation

3.58351 \dots

Solution steps

2 ln (6 x) - \frac{2}{3} ln (x^{3})

Apply log rule:

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

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

= ln ((6 x)^{2}) - \frac{2}{3} ln (x^{3})

Apply log rule:

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

\frac{2}{3} ln (x^{3}) = ln ((x^{3})^{\frac{2}{3}})

= ln ((6 x)^{2}) - ln ((x^{3})^{\frac{2}{3}})

Apply log rule:

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

ln ((6 x)^{2}) - ln ((x^{3})^{\frac{2}{3}}) = ln (\frac{( 6 x ) ^{2}}{( x ^{3} ) ^{\frac{2}{3}}})

= ln (\frac{( 6 x ) ^{2}}{( x ^{3} ) ^{\frac{2}{3}}})

\frac{( 6 x ) ^{2}}{( x ^{3} ) ^{\frac{2}{3}}} = 36

= ln (36)

Rewrite

36

in power-base form:

36 = 6^{2}

= ln (6^{2})

Apply log rule:

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

ln (6^{2}) = 2 ln (6)

= 2 ln (6)

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Frequently Asked Questions (FAQ)

What is 2ln(6x)-2/3 ln(x^3) ?
The solution to 2ln(6x)-2/3 ln(x^3) is 2ln(6)