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Sagot :
Step-by-step explanation:
To write the equation in LaTeX in form y = ab^x or [tex]ab^x[/tex] for y = abx .........(1)
(a) LaTeX: y=3\sqrt{4^{2x}} y = 3 4 2 x can be written in mathematical form as
[tex]y=3\sqrt{4^{2x}}[/tex] ; y = 342x
on comparing with equation (1) we get a =3 and b =4
⇒y = 34^x or [tex]34^x[/tex]
(b) LaTeX: y=\frac{\sqrt[3]{5^{3x}}}{2} y = 5 3 x 3 2 can be written in mathematical form as
[tex]y=\frac{\sqrt[3]{5^{3x}}}{2}[/tex] ; y = 342x
on comparing with equation (1) we get a =0.5 and b =5
⇒y = [tex]\frac{1}{2}5^x[/tex]
(c)LaTeX: y=8^{x+2} y = 8 x + 2 can be written in mathematical form as
[tex]y=8^{x+2}[/tex]
on comparing with equation (1) we get a =64 and b =8
y = [tex]64 . 8^x[/tex]
(d)LaTeX: y=\frac{3^{2x+1}}{\sqrt{3^{2x}}} can be written in mathematical form as
[tex]y=\frac{3^{2x+1}}{\sqrt{3^{2x}}}[/tex] = [tex]3^{x+1}[/tex] = [tex]3 . 3^x[/tex]
on comparing with equation (1) we get a =3 and b =3
y = [tex]3 . 3^x[/tex]
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