Question

a)(7x - 11)³ = 2⁵. 5² + 200

b)3² .x² - 2².x^{2 =3}5^{. 5} - (255: 51) . 11

c) 5^4x. 5¹⁴ =5⁷⁸

d) 3³ . x² - 2^4. x²= 8² . 5 - 4² . 3²

e) (3x - 6) .3 =3⁵

Answer 1

\(a,\left(7x-11\right)^3=2^5.5^2+200\)

\(\Leftrightarrow\left(7x-11\right)^3=32.25+200\)

\(\Leftrightarrow\left(7x-11\right)^3=800+200\)

\(\Leftrightarrow\left(7x-11\right)^3=1000\)

\(\Leftrightarrow\left(7x-11\right)^3=10^3\)

\(\Rightarrow7x-11=10\)

\(\Rightarrow7x=21\)

\(\Rightarrow x=3\)

Answer 2

\(b,3^2.x^2-2^2.x^2=5^5-\left(255:51\right).11\)

\(\Rightarrow x^2\left(3^2-2^2\right)=3125-5.11\)

\(\Rightarrow x^2\left(9-4\right)=3125-55\)

\(\Rightarrow5x^2=2970\)

\(\Rightarrow x^2=2970:5\)

\(\Rightarrow x^2=594\)

\(\Rightarrow x=3\sqrt{66}\)

Answer 3

\(c,5^{4x}.5^{14}=5^{78}\)

\(\Rightarrow4x+14=78\)

\(\Rightarrow4x=78-14\)

\(\Rightarrow4x=64\)

\(\Rightarrow x=16\)

Answer 4

\(d,3^3.x^2-2^4.x^2=8^2.5-4^2.3^2\)

\(\Rightarrow x^2\left(3^3-2^4\right)=64.5-16.3\)

\(\Rightarrow x^2\left(27-16\right)=320-48\)

\(\Rightarrow11x^2=272\)

\(\Rightarrow x^2=\frac{272}{11}\)

\(\Rightarrow\frac{4\sqrt{187}}{11}\)

Answer 5

\(e,\left(3x-6\right).3=3^5\)

\(\Rightarrow\left(3x-6\right).3=243\)

\(\Rightarrow3x-6=81\)

\(\Rightarrow3x=87\)

\(\Rightarrow x=29\)