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Popular >

simplify 3ln(10)-ln(8)

Solution

simplify

3 ln (10) - ln (8)

Solution

3 ln (5)

+1

Decimal Notation

4.82831 \dots

Solution steps

3 ln (10) - ln (8)

Apply log rule:

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

3 ln (10) = ln (1 0^{3})

= ln (1 0^{3}) - ln (8)

Apply log rule:

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

ln (1 0^{3}) - ln (8) = ln (\frac{1 0 ^{3}}{8})

= ln (\frac{1 0 ^{3}}{8})

\frac{1 0 ^{3}}{8} = 125

= ln (125)

Rewrite

125

in power-base form:

125 = 5^{3}

= ln (5^{3})

Apply log rule:

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

ln (5^{3}) = 3 ln (5)

= 3 ln (5)

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Frequently Asked Questions (FAQ)

What is 3ln(10)-ln(8) ?
The solution to 3ln(10)-ln(8) is 3ln(5)