What is 2ln(a)-1/2 ln(b) ?

The solution to 2ln(a)-1/2 ln(b) is ln((a^2sqrt(b))/b)

Popular >

simplify 2ln(a)-1/2 ln(b)

simplify

2 ln (a) - \frac{1}{2} ln (b)

ln (\frac{a ^{2} b}{b})

Solution steps

2 ln (a) - \frac{1}{2} ln (b)

Apply log rule:

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

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

= ln (a^{2}) - \frac{1}{2} ln (b)

Apply log rule:

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

\frac{1}{2} ln (b) = ln (b^{\frac{1}{2}})

= ln (a^{2}) - ln (b^{\frac{1}{2}})

Apply log rule:

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

ln (a^{2}) - ln (b^{\frac{1}{2}}) = ln (\frac{a ^{2}}{b ^{\frac{1}{2}}})

= ln (\frac{a ^{2}}{b ^{\frac{1}{2}}})

Simplify

\frac{a ^{2}}{b ^{\frac{1}{2}}} : \frac{a ^{2} b}{b}

= ln (\frac{a ^{2} b}{b})

5.8 + lo g_{10} (\frac{0.015}{0.4})

ln ∣ x ∣ + ln ∣ sin (x) ∣

lo g_{10} (6.5 x 1 0^{7}) - lo g_{10} (1000)

\frac{1}{2} ln (\frac{e + e ^{2} - 1}{e - e ^{2} - 1})

6 \cdot ln (3) - 6 \cdot ln (2)

What is 2ln(a)-1/2 ln(b) ?
The solution to 2ln(a)-1/2 ln(b) is ln((a^2sqrt(b))/b)