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Popular >

simplify ln(5)-2ln(6)-ln(25)

Solution

simplify

ln (5) - 2 ln (6) - ln (25)

Solution

- ln (180)

+1

Decimal Notation

- 5.19295 \dots

Solution steps

ln (5) - 2 ln (6) - ln (25)

Apply log rule:

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

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

= ln (5) - ln (6^{2}) - ln (25)

Apply log rule:

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

ln (5) - ln (6^{2}) = ln (\frac{5}{6 ^{2}})

= ln (\frac{5}{6 ^{2}}) - ln (25)

6^{2} = 36

= ln (\frac{5}{36}) - ln (25)

Apply log rule:

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

ln (\frac{5}{36}) - ln (25) = ln (\frac{\frac{5}{36}}{25})

= ln (\frac{\frac{5}{36}}{25})

\frac{\frac{5}{36}}{25} = \frac{1}{180}

= ln (\frac{1}{180})

Apply log rule:

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

= - ln (180)

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Frequently Asked Questions (FAQ)

What is ln(5)-2ln(6)-ln(25) ?
The solution to ln(5)-2ln(6)-ln(25) is -ln(180)