a) x : \(\left(\dfrac{3}{4}\right)^3=\left(\dfrac{3}{4}\right)^2\)

x = \(\left(\dfrac{3}{4}\right)^2.\left(\dfrac{3}{4}\right)^3\)

x =\(\left(\dfrac{3}{4}\right)^5\)

Vậy x =\(\left(\dfrac{3}{4}\right)^5\)

b) \(\left(\dfrac{2}{5}\right)^5.x=\left(\dfrac{2}{5}\right)^8\)

\(x=\left(\dfrac{2}{5}\right)^8:\left(\dfrac{2}{5}\right)^5\)

\(x=\left(\dfrac{2}{5}\right)^3\)

Vậy \(x=\left(\dfrac{2}{5}\right)^3\)

1 Tìm x biết :

a) \(\left(5x+1\right)^2\) = \(\dfrac{36}{49}\)

b) \(\left(x-\dfrac{2}{9}\right)^3\) = \(\left(\dfrac{2}{3}\right)^6\)

c) \(\left(8x-1\right)^{2n+1}\) = \(5^{2n+1}\) \(\left(n\in N\right)\)

a) \(\left(5x+1\right)^2=\dfrac{36}{49}\)

\(\left(5x+1\right)^2=\left(\pm\dfrac{6}{9}\right)\)\(^2\)

\(5x+1=\pm\dfrac{6}{9}\)

+) \(5x+1=\dfrac{6}{9}\)

\(5x=\dfrac{6}{9}-1=\dfrac{6}{9}-\dfrac{9}{9}\)

\(5x=\dfrac{-5}{9}\)

\(x=\dfrac{-5}{9}:5=\dfrac{-1}{45}\)

+) \(5x+1=\dfrac{-6}{9}\)

\(5x=\dfrac{-6}{9}-1=\dfrac{-6}{9}-\dfrac{9}{9}\)

\(5x=\dfrac{-5}{3}\)

\(x=\dfrac{-5}{3}:5=\dfrac{-5}{15}\)

vậy \(x\in\left\{\dfrac{-5}{15};\dfrac{-1}{45}\right\}\)

Bài 1: Tìm x

a) \(\left(x-2\right)^4=256\)

b) \(\frac{x^4}{256}=81\)

c) \(125\left(x+\frac{4}{5}\right)^3=729\)

e) \(7^x+2+7x=50\)

f) \(9.13^{x-1}+\frac{4}{169}.13^{x+1}=2197\)

c) \(125\left(x+\dfrac{4}{5}\right)^3=729\)

\(\left(x+\dfrac{4}{5}\right)^3=729:125=\dfrac{729}{125}\)

\(\left(x+\dfrac{4}{5}\right)^3=\left(\dfrac{9}{5}\right)^3\)

\(x+\dfrac{4}{5}=\dfrac{9}{5}\)

x = \(\dfrac{9}{5}-\dfrac{4}{5}\)

x \(=1\)