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人気のある代数 >

4sqrt(x+1)=2^{3x-2}

解

4 x + 1 = 2^{3 x - 2}

解

x = - \frac{W _{- 1} ( - \frac{3 l n ( 2 )}{8192} ) + 6 ln ( 2 )}{6 ln ( 2 )}, x = - \frac{W _{0} ( - \frac{3 l n ( 2 )}{8192} ) + 6 ln ( 2 )}{6 ln ( 2 )}

+1

十進法表記

x = 1.55929 \dots, x = - 0.99993 \dots

解答ステップ

4 x + 1 = 2^{3 x - 2}

ランベルト形式向けに

4 x + 1 = 2^{3 x - 2}

を準備する:

e^{l n (2) (- 6 x + 8)} (x + 1) = 1

equationを

(- 6 x - 6) ln (2) = u

と以下で書き換える:

x = - \frac{u + 6 ln ( 2 )}{6 ln ( 2 )}

e^{l n (2) (- 6 (- \frac{u + 6 l n ( 2 )}{6 l n ( 2 )}) + 8)} ((- \frac{u + 6 ln ( 2 )}{6 ln ( 2 )}) + 1) = 1

簡素化

e^{u + 14 l n (2)} (- \frac{u + 6 ln ( 2 )}{6 ln ( 2 )} + 1) = 1

ランベルト形式で

e^{u + 14 l n (2)} (- \frac{u + 6 ln ( 2 )}{6 ln ( 2 )} + 1) = 1

を書き換える:

e^{u} u = - \frac{3 ln ( 2 )}{8192}

解く

e^{u} u = - \frac{3 ln ( 2 )}{8192} : u = W_{- 1} (- \frac{3 ln ( 2 )}{8192}), u = W_{0} (- \frac{3 ln ( 2 )}{8192})

u = W_{- 1} (- \frac{3 ln ( 2 )}{8192}), u = W_{0} (- \frac{3 ln ( 2 )}{8192})

再び

u = (- 6 x - 6) ln (2)

に置き換えて以下を解く:

x

解く

(- 6 x - 6) ln (2) = W_{- 1} (- \frac{3 ln ( 2 )}{8192}) : x = - \frac{W _{- 1} ( - \frac{3 l n ( 2 )}{8192} ) + 6 ln ( 2 )}{6 ln ( 2 )}

解く

(- 6 x - 6) ln (2) = W_{0} (- \frac{3 ln ( 2 )}{8192}) : x = - \frac{W _{0} ( - \frac{3 l n ( 2 )}{8192} ) + 6 ln ( 2 )}{6 ln ( 2 )}

x = - \frac{W _{- 1} ( - \frac{3 l n ( 2 )}{8192} ) + 6 ln ( 2 )}{6 ln ( 2 )}, x = - \frac{W _{0} ( - \frac{3 l n ( 2 )}{8192} ) + 6 ln ( 2 )}{6 ln ( 2 )}

解を検算する:

x = - \frac{W _{- 1} ( - \frac{3 l n ( 2 )}{8192} ) + 6 ln ( 2 )}{6 ln ( 2 )}

真

, x = - \frac{W _{0} ( - \frac{3 l n ( 2 )}{8192} ) + 6 ln ( 2 )}{6 ln ( 2 )}

真

解答は

x = - \frac{W _{- 1} ( - \frac{3 l n ( 2 )}{8192} ) + 6 ln ( 2 )}{6 ln ( 2 )}, x = - \frac{W _{0} ( - \frac{3 l n ( 2 )}{8192} ) + 6 ln ( 2 )}{6 ln ( 2 )}

解を検算する:

x = - \frac{W _{- 1} ( - \frac{3 l n ( 2 )}{8192} ) + 6 ln ( 2 )}{6 ln ( 2 )}

真

, x = - \frac{W _{0} ( - \frac{3 l n ( 2 )}{8192} ) + 6 ln ( 2 )}{6 ln ( 2 )}

真

解答は

x = - \frac{W _{- 1} ( - \frac{3 l n ( 2 )}{8192} ) + 6 ln ( 2 )}{6 ln ( 2 )}, x = - \frac{W _{0} ( - \frac{3 l n ( 2 )}{8192} ) + 6 ln ( 2 )}{6 ln ( 2 )}

グラフ

人気の例

e^{-4k-10}= 67/6

e^{- 4 k - 10} = \frac{67}{6}

3^{x} = 5^{x + 2}

(a^3)^6=(a^2)^x

(a^{3})^{6} = (a^{2})^{x}

solvefor x,4^{x+1}+2^y=20

so l v e f or x, 4^{x + 1} + 2^{y} = 20

solvefor t,(1.045)^t=2

so l v e f or t, (1.045)^{t} = 2