What is 3ln(1000)-2log_{4}(1/64)+6ln(e) ?

The solution to 3ln(1000)-2log_{4}(1/64)+6ln(e) is 9ln(10)+12

Popular >

simplify 3ln(1000)-2log_{4}(1/64)+6ln(e)

simplify

3 ln (1000) - 2 lo g_{4} (\frac{1}{64}) + 6 ln (e)

9 ln (10) + 12

Decimal Notation

32.72326 \dots

Solution steps

3 ln (1000) - 2 lo g_{4} (\frac{1}{64}) + 6 ln (e)

Apply log rule:

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

lo g_{4} (\frac{1}{64}) = lo g_{4} (1) - lo g_{4} (64)

= 3 ln (1000) - 2 (lo g_{4} (1) - lo g_{4} (64)) + 6 ln (e)

2 (lo g_{4} (1) - lo g_{4} (64)) = - 6

6 ln (e) = 6

= 3 ln (1000) - (- 6) + 6

Apply rule

- (- a) = a

= 3 ln (1000) + 6 + 6

Add the numbers:

6 + 6 = 12

= 3 ln (1000) + 12

3 ln (1000) = 9 ln (10)

= 9 ln (10) + 12

ln (8) - \frac{1}{2} ln (k) - 3 ln (t) - \frac{1}{3} ln (m)

- lo g_{10} (2.3 \cdot 1 0^{- 3})

ln ∣ x ∣ - ln ∣ y ∣

ln (x^{2} + 1) (ln (4 x^{2} + 6) - ln (x^{4} + 1))

ln (a) - 3 ln (b) + 4 ln (c)

What is 3ln(1000)-2log_{4}(1/64)+6ln(e) ?
The solution to 3ln(1000)-2log_{4}(1/64)+6ln(e) is 9ln(10)+12