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Popular >

simplify log_{e}(1/3 e^{3x+1})

Solution

simplify

lo g_{e} (\frac{1}{3} e^{3 x + 1})

Solution

3 x + 1 - ln (3)

Solution steps

lo g_{e} (\frac{1}{3} e^{3 x + 1})

Apply log rule:

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

lo g_{e} (\frac{1}{3} e^{3 x + 1}) = lo g_{e} (\frac{1}{3}) + lo g_{e} (e^{3 x + 1})

= lo g_{e} (\frac{1}{3}) + lo g_{e} (e^{3 x + 1})

Apply log rule:

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

lo g_{e} (e^{3 x + 1}) = (3 x + 1) lo g_{e} (e)

= lo g_{e} (\frac{1}{3}) + (3 x + 1) lo g_{e} (e)

Apply log rule:

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

lo g_{e} (\frac{1}{3}) = lo g_{e} (1) - lo g_{e} (3)

= lo g_{e} (1) - lo g_{e} (3) + lo g_{e} (e) (3 x + 1)

lo g_{e} (1) = 0

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

(3 x + 1) lo g_{e} (e) = 3 x + 1

= 0 - ln (3) + 3 x + 1

Group like terms

= 3 x - ln (3) + 0 + 1

Add the numbers:

0 + 1 = 1

= 3 x + 1 - ln (3)

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Frequently Asked Questions (FAQ)

What is log_{e}(1/3 e^{3x+1}) ?
The solution to log_{e}(1/3 e^{3x+1}) is 3x+1-ln(3)