Question

tentukan nilai x yg memenuhi
a) 2^3x=4^2x-1
b) 4^2x-1=8

tolong dibantu kak
​

Answer 1

Jawaban:

Bagian a.

[tex]\begin{aligned}\sf {2}^{3x} &= \sf {4}^{2x - 1} \\ \sf {2}^{3x} &= \sf ( {2}^{2}) {}^{2x - 1} \\ \sf {2}^{3x} &= \sf {2}^{4x -2 } \\ \sf \cancel{2} {}^{3x} &= \sf \cancel{2} {}^{4x - 2} \\ \sf 3x &= \sf 4x - 2 \\ \sf 3x - 4x&= \sf - 2 \\ \sf - x&= \sf - 2 \\ \sf x&= \sf \frac{ - 2}{ - 1} \\ \sf x&= \sf \red{2}\end{aligned}[/tex]

Bagian b.

[tex]\begin{aligned}\sf {4}^{2x - 1} &= \sf 8 \\ \sf ( {2}^{2}) {}^{2x - 1}&= \sf {2}^{3} \\ \sf {2}^{4x - 2} &= \sf {2}^{3} \\ \sf \cancel{2} {}^{4x - 2} &= \sf \cancel{2} {}^{3} \\ \sf 4x - 2&= \sf 3 \\ \sf 4x &= \sf 3 + 2 \\ \sf 4x&= \sf 5 \\ \sf x&= \sf \red{ \frac{5}{4}} \end{aligned}[/tex]

'조슈아' (Svt)

Answer 2

Penjelasan dengan langkah-langkah:

a)

[tex] {2}^{3 \text{x}} = {4}^{2 \text{x} - 1} [/tex]

[tex] {2}^{3 \text{x} } = { ({2}^{2} )}^{2 \text{x} - 1} [/tex]

[tex] { \cancel2}^{3 \text{x}} = { \cancel2}^{4 \text{x} - 2} [/tex]

[tex]3 \text{x} = 4 \text{x} - 2[/tex]

[tex]3 \text{x} - 4 \text{x} = - 2[/tex]

[tex] - \text{x} = - 2[/tex]

[tex] \text{x} = \bold2[/tex]

b)

[tex] {4}^{2 \text{x} - 1} = 8[/tex]

[tex] { ({2}^{2}) }^{2 \text{x} - 1} = {2}^{3} [/tex]

[tex] { \cancel2}^{4 \text{x} - 2} = { \cancel2}^{3} [/tex]

[tex]4 \text{x} - 2 = 3[/tex]

[tex]4 \text{x} = 3 + 2[/tex]

[tex]4 \text{x} = 5[/tex]

[tex] \text{x} = \bold{ \frac{5}{4}} [/tex]