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Popular >

simplify log_{e}(4e^{3x})

Solution

simplify

lo g_{e} (4 e^{3 x})

Solution

2 ln (2) + 3 x

Solution steps

lo g_{e} (4 e^{3 x})

Apply log rule:

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

lo g_{e} (4 e^{3 x}) = lo g_{e} (4) + lo g_{e} (e^{3 x})

= lo g_{e} (4) + lo g_{e} (e^{3 x})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{e} (e^{3 x}) = 3 x lo g_{e} (e)

= lo g_{e} (4) + 3 x lo g_{e} (e)

lo g_{e} (4) = ln (4)

3 x lo g_{e} (e) = 3 x

= ln (4) + 3 x

ln (4) = 2 ln (2)

= 2 ln (2) + 3 x

Popular Examples

simplify 5log_{10}(X)+4log_{10}(Y)simplify

5 lo g_{10} (X) + 4 lo g_{10} (Y)

simplify ln(10)+ln(10)-ln(5)-ln(15)simplify

ln (10) + ln (10) - ln (5) - ln (15)

simplify-log_{10}(3.16*10^2)simplify

- lo g_{10} (3.16 \cdot 1 0^{2})

domain of f(x)=2x^2+ln(3x)domain

f (x) = 2 x^{2} + ln (3 x)

simplify-log_{10}(1.15*10^{-15})simplify

- lo g_{10} (1.15 \cdot 1 0^{- 15})

Frequently Asked Questions (FAQ)

What is log_{e}(4e^{3x}) ?
The solution to log_{e}(4e^{3x}) is 2ln(2)+3x