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人気のある代数 >

(x+1)=log_{10}(x-1)+3

解

(x + 1) = lo g_{10} (x - 1) + 3

解

x = 2, x = - \frac{W _{0} ( - \frac{l n ( 10 )}{10} ) - ln ( 10 )}{ln ( 10 )}

+1

十進法表記

x = 2, x = 1.13712 \dots

解答ステップ

(x + 1) = lo g_{10} (x - 1) + 3

辺を交換する

lo g_{10} (x - 1) + 3 = x + 1

3

を右側に移動します

lo g_{10} (x - 1) = x - 2

f (x) = g (x)

ならば,

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

1 0^{l o g_{10} (x - 1)} = 1 0^{x - 2}

簡素化

1 0^{l o g_{10} (x - 1)} : x - 1

x - 1 = 1 0^{x - 2}

解く

x - 1 = 1 0^{x - 2} : x = 2, x = - \frac{W _{0} ( - \frac{l n ( 10 )}{10} ) - ln ( 10 )}{ln ( 10 )}

x = 2, x = - \frac{W _{0} ( - \frac{l n ( 10 )}{10} ) - ln ( 10 )}{ln ( 10 )}

解を検算する:

x = 2

真

, x = - \frac{W _{0} ( - \frac{l n ( 10 )}{10} ) - ln ( 10 )}{ln ( 10 )}

真

解答は

x = 2, x = - \frac{W _{0} ( - \frac{l n ( 10 )}{10} ) - ln ( 10 )}{ln ( 10 )}

グラフ

人気の例

log_{4}(x+20)=3

lo g_{4} (x + 20) = 3

ln(x)-ln(x+1)=5

ln (x) - ln (x + 1) = 5

5=log_{3}(x^2+18)

5 = lo g_{3} (x^{2} + 18)

6+log_{10}(x)-log_{2}(x)=0

6 + lo g_{10} (x) - lo g_{2} (x) = 0

log_{10}((4-2x)/(2x))=1

lo g_{10} (\frac{4 - 2 x}{2 x}) = 1