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人気のある代数 >

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

解

lo g_{3} (4 - 3^{x - 1} - 1) = 2 x - 1

解

x = \frac{ln ( \frac{- 1 + 37}{2} )}{ln ( 3 )}

+1

十進法表記

x = 0.84898 \dots

解答ステップ

lo g_{3} (4 - 3^{x - 1} - 1) = 2 x - 1

f (x) = g (x)

ならば,

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

3^{l o g_{3} (4 - 3^{x - 1} - 1)} = 3^{2 x - 1}

簡素化

3^{l o g_{3} (4 - 3^{x - 1} - 1)} : 3 - 3^{x - 1}

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

解く

3 - 3^{x - 1} = 3^{2 x - 1} : x = \frac{ln ( \frac{- 1 + 37}{2} )}{ln ( 3 )}

x = \frac{ln ( \frac{- 1 + 37}{2} )}{ln ( 3 )}

解を検算する:

x = \frac{ln ( \frac{- 1 + 37}{2} )}{ln ( 3 )}

真

解は

x = \frac{ln ( \frac{- 1 + 37}{2} )}{ln ( 3 )}

グラフ

人気の例

lo g_{3} (x) = 10

6log_{5}(x)+7log_{2}(x)=6

6 lo g_{5} (x) + 7 lo g_{2} (x) = 6

ln(x-2)+ln(x)=0

ln (x - 2) + ln (x) = 0

0.3=log_{10}(x)

0.3 = lo g_{10} (x)

log_{x+1}((x^2+x-6)^2)=4

lo g_{x + 1} ((x^{2} + x - 6)^{2}) = 4