What is ln(5)-2ln(4)+ln(32) ?

The solution to ln(5)-2ln(4)+ln(32) is ln(10)

Popular >

simplify ln(5)-2ln(4)+ln(32)

simplify

ln (5) - 2 ln (4) + ln (32)

ln (10)

Decimal Notation

2.30258 \dots

Solution steps

ln (5) - 2 ln (4) + ln (32)

Apply log rule:

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

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

= ln (5) - ln (4^{2}) + ln (32)

Apply log rule:

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

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

= ln (\frac{5}{4 ^{2}}) + ln (32)

4^{2} = 16

= ln (\frac{5}{16}) + ln (32)

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln (\frac{5}{16}) + ln (32) = ln (32 \cdot \frac{5}{16})

= ln (32 \cdot \frac{5}{16})

\frac{5}{16} \cdot 32 = 10

= ln (10)

ln (\frac{m ^{3}}{b ^{2}})

ln (\frac{1}{125}) + 4 ln (5) - 2 ln (\frac{1}{5})

ln (\frac{1}{x}) - ln (x)

\frac{6}{5} ln \frac{y}{x} - 1 - \frac{1}{5} ln \frac{y}{x} + 4 + ln ∣ x ∣

0.77 + \frac{8.134 \cdot 298}{1 \cdot 96500} \cdot ln (\frac{1}{4})