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人気のある代数 >

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

解

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

解

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

十進法表記

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

解答ステップ

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

以下で両辺を割る

3

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

f (x) = g (x)

ならば,

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

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

簡素化

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

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

解く

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 )}

解を検算する:

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

真

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

真

解答は

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 )}

グラフ

人気の例

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

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

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

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

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

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

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

log_{8}(x^2-7x)=1

lo g_{8} (x^{2} - 7 x) = 1