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Popular >

simplify 9ln(x)-3ln(2x^3)

Solution

simplify

9 ln (x) - 3 ln (2 x^{3})

Solution

- 3 ln (2)

+1

Solution steps

9 ln (x) - 3 ln (2 x^{3})

Apply log rule:

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

9 ln (x) = ln (x^{9})

= ln (x^{9}) - 3 ln (2 x^{3})

Apply log rule:

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

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

= ln (x^{9}) - ln ((2 x^{3})^{3})

Apply log rule:

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

ln (x^{9}) - ln ((2 x^{3})^{3}) = ln (\frac{x ^{9}}{( 2 x ^{3} ) ^{3}})

= ln (\frac{x ^{9}}{( 2 x ^{3} ) ^{3}})

\frac{x ^{9}}{( 2 x ^{3} ) ^{3}} = \frac{1}{8}

= ln (\frac{1}{8})

Apply log rule:

lo g_{a} (\frac{1}{x}) = - lo g_{a} (x)

= - ln (8)

Rewrite

8

in power-base form:

8 = 2^{3}

= - ln (2^{3})

Apply log rule:

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

ln (2^{3}) = 3 ln (2)

= - 3 ln (2)

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Frequently Asked Questions (FAQ)

What is 9ln(x)-3ln(2x^3) ?
The solution to 9ln(x)-3ln(2x^3) is -3ln(2)