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Popular >

simplify 3ln(3)-3ln(0.5)

Solution

simplify

3 ln (3) - 3 ln (0.5)

Solution

3 ln (6)

+1

Solution steps

3 ln (3) - 3 ln (0.5)

Apply log rule:

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

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

= ln (3^{3}) - 3 ln (0.5)

Apply log rule:

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

3 ln (0.5) = ln (0. 5^{3})

= ln (3^{3}) - ln (0. 5^{3})

Apply log rule:

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

ln (3^{3}) - ln (0. 5^{3}) = ln (\frac{3 ^{3}}{0. 5 ^{3}})

= ln (\frac{3 ^{3}}{0. 5 ^{3}})

\frac{3 ^{3}}{0. 5 ^{3}} = 216

= ln (216)

Rewrite

216

in power-base form:

216 = 6^{3}

= ln (6^{3})

Apply log rule:

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

ln (6^{3}) = 3 ln (6)

= 3 ln (6)

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Frequently Asked Questions (FAQ)

What is 3ln(3)-3ln(0.5) ?
The solution to 3ln(3)-3ln(0.5) is 3ln(6)