Question

a) (3x-5)^4=81        b) (7-3x)^2+15=16           c) (4-3x)^3 +15=7       d) (2x-3)^3-14=50       e) 3^7-x =243             g) 2^4x-5 =8             h) 5^x+1 +2*5^x=875       i) 3^x+2 + 3^x+1-5*3^x =567

Answer 1

a: =>3x-5=3 hoặc 3x-5=-3

=>3x=8 hoặc 3x=2

=>x=8/3 hoặc x=2/3

b: =>(3x-7)²=1

=>3x-7=1 hoặc 3x-7=-1

=>3x=8 hoặc 3x=6

=>x=8/3 hoặc x=2

e: =>7-x=5

hay x=2

g: =>4x-5=3

=>4x=8

hay x=2

Answer 2

\(\left(3x-5\right)^4=81.\\\Leftrightarrow\left[{}\begin{matrix}\left(3x-5\right)^4=3^4.\\\left(3x-5\right)^4=\left(-3\right)^4.\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}3x-5=3.\\3x-5=-3.\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{8}{3}.\\x=\dfrac{2}{3}.\end{matrix}\right.\)

\(\left(7-3x\right)^2+15=16.\\ \Leftrightarrow\left(7-3x\right)^2=1.\\ \Leftrightarrow\left[{}\begin{matrix}7-3x=1.\\7-3x=-1.\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=2.\\x=\dfrac{8}{3}.\end{matrix}\right.\)

\(\left(4-3x\right)^3+15=7.\\ \Leftrightarrow\left(4-3x\right)^3=-8.\\ \Leftrightarrow\left(4-3x\right)^3=\left(-2\right)^3.\\ \Leftrightarrow4-3x=-2.\\ \Leftrightarrow x=2.\)

\(\left(2x-3\right)^3-14=50.\\ \Leftrightarrow\left(2x-3\right)^3=64.\\ \Leftrightarrow\left(2x-3\right)^3=4^3.\\ \Leftrightarrow2x-3=4.\\ \Leftrightarrow x=\dfrac{7}{2}.\)

\(3^7-x=243.\\ \Leftrightarrow x=3^7-243=1944.\)