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Popular >

simplify 3ln(10)-4ln(2)-ln(5)

Solution

simplify

3 ln (10) - 4 ln (2) - ln (5)

Solution

ln (\frac{25}{2})

+1

Decimal Notation

2.52572 \dots

Solution steps

3 ln (10) - 4 ln (2) - ln (5)

Apply log rule:

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

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

= ln (1 0^{3}) - 4 ln (2) - ln (5)

Apply log rule:

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

4 ln (2) = ln (2^{4})

= ln (1 0^{3}) - ln (2^{4}) - ln (5)

Apply log rule:

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

ln (1 0^{3}) - ln (2^{4}) = ln (\frac{1 0 ^{3}}{2 ^{4}})

= ln (\frac{1 0 ^{3}}{2 ^{4}}) - ln (5)

\frac{1 0 ^{3}}{2 ^{4}} = \frac{125}{2}

= ln (\frac{125}{2}) - ln (5)

Apply log rule:

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

ln (\frac{125}{2}) - ln (5) = ln (\frac{\frac{125}{2}}{5})

= ln (\frac{\frac{125}{2}}{5})

\frac{\frac{125}{2}}{5} = \frac{25}{2}

= ln (\frac{25}{2})

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Frequently Asked Questions (FAQ)

What is 3ln(10)-4ln(2)-ln(5) ?
The solution to 3ln(10)-4ln(2)-ln(5) is ln(25/2)