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Popular >

3log_{3}(n+2)=2n-3

Solution

3 lo g_{3} (n + 2) = 2 n - 3

Solution

n = - \frac{3 W _{- 1} ( - \frac{2 l n ( 3 )}{3 e ^{\frac{7 l n ( 3 )}{3}}} ) + 4 ln ( 3 )}{2 ln ( 3 )}, n = - \frac{3 W _{0} ( - \frac{2 l n ( 3 )}{3 e ^{\frac{7 l n ( 3 )}{3}}} ) + 4 ln ( 3 )}{2 ln ( 3 )}

+1

Decimal

n = 3.93048 \dots, n = - 1.91820 \dots

Solution steps

3 lo g_{3} (n + 2) = 2 n - 3

Divide both sides by

3

lo g_{3} (n + 2) = \frac{2 n - 3}{3}

If

f (x) = g (x),

then

a^{f (x)} = a^{g (x)}

3^{l o g_{3} (n + 2)} = 3^{\frac{2 n - 3}{3}}

Simplify

3^{l o g_{3} (n + 2)} : n + 2

n + 2 = 3^{\frac{2 n - 3}{3}}

Solve

n + 2 = 3^{\frac{2 n - 3}{3}} : n = - \frac{3 W _{- 1} ( - \frac{2 l n ( 3 )}{3 e ^{\frac{7 l n ( 3 )}{3}}} ) + 4 ln ( 3 )}{2 ln ( 3 )}, n = - \frac{3 W _{0} ( - \frac{2 l n ( 3 )}{3 e ^{\frac{7 l n ( 3 )}{3}}} ) + 4 ln ( 3 )}{2 ln ( 3 )}

n = - \frac{3 W _{- 1} ( - \frac{2 l n ( 3 )}{3 e ^{\frac{7 l n ( 3 )}{3}}} ) + 4 ln ( 3 )}{2 ln ( 3 )}, n = - \frac{3 W _{0} ( - \frac{2 l n ( 3 )}{3 e ^{\frac{7 l n ( 3 )}{3}}} ) + 4 ln ( 3 )}{2 ln ( 3 )}

Verify Solutions:

n = - \frac{3 W _{- 1} ( - \frac{2 l n ( 3 )}{3 e ^{\frac{7 l n ( 3 )}{3}}} ) + 4 ln ( 3 )}{2 ln ( 3 )}

True

, n = - \frac{3 W _{0} ( - \frac{2 l n ( 3 )}{3 e ^{\frac{7 l n ( 3 )}{3}}} ) + 4 ln ( 3 )}{2 ln ( 3 )}

True

The solutions are

n = - \frac{3 W _{- 1} ( - \frac{2 l n ( 3 )}{3 e ^{\frac{7 l n ( 3 )}{3}}} ) + 4 ln ( 3 )}{2 ln ( 3 )}, n = - \frac{3 W _{0} ( - \frac{2 l n ( 3 )}{3 e ^{\frac{7 l n ( 3 )}{3}}} ) + 4 ln ( 3 )}{2 ln ( 3 )}

Graph

Popular Examples

ln(sqrt(x-4))=6

ln (x - 4) = 6

lo g_{3} (x + 1) = 4

log_{8}(7-5w)+2= 11/3

lo g_{8} (7 - 5 w) + 2 = \frac{11}{3}

lo g_{4} (\frac{7}{x}) = 3

log_{5}(3x+10)=2

lo g_{5} (3 x + 10) = 2

Frequently Asked Questions (FAQ)

What is the answer to 3log_{3}(n+2)=2n-3 ?
The answer to 3log_{3}(n+2)=2n-3 is
Solve for n: 3log_{3}(n+2)=2n-3
The solution is