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RoseWind [281]
3 years ago
8

Rewrite the given expression in the form 3^u where u is a constant or an algebraic expression.

Mathematics
2 answers:
lawyer [7]3 years ago
8 0
Simplifying the given expressions we proceed as follows:
(5sqrt3)^x
=5^x*(3^1/2)^x
=5^x*3^x/2
=5^x3^u
where u=x/2


(1/2)^(x-3)
=1/2^(x-3)
=2^-(3-x)
=2^u
where u=-(3-x)

9/3sqrt(3)
=3/(3)^(1/2)
=3(3)^(-1/2)

16/(3sqrt (2^x))
=1/3*(2^4*2^(-x/2))
=1/3*2^(4-x/2)
=1/3*2^u
where:
u=4-x/2

geniusboy [140]3 years ago
3 0

Solution: (1) The expression (5\sqrt{3} )^x  \text{ is written as } 5^x3^{\frac{x}{2}.

(5\sqrt{3} )^x=5^x(\sqrt{3} )^x\\(5\sqrt{3} )^x=5^x(3^\frac{1}{2} )^x\\(5\sqrt{3} )^x=5^x3^\frac{x}{2}

The value of u is \frac{x}{2}.

(2) The expression (\frac{1}{2})^x-3 is written as 2^{-x}-3.

(\frac{1}{2})^x-3=(2^{-1})^x-3\\(\frac{1}{2})^x-3=2^{-x}-3

The value of u is -x.

(3) The expression \frac{9}{3\sqrt{3} } is written as \sqrt{3} (2^0).

\frac{9}{3\sqrt{3} }=\frac{9}{3\sqrt{3} }(\frac{\sqrt{3}}{\sqrt{3}} )\\\frac{9}{3\sqrt{3} }=\frac{9(\sqrt{3}) }{3(3) }\\\frac{9}{3\sqrt{3} }=\sqrt{3} \\\frac{9}{3\sqrt{3} }=\sqrt{3}(2^0)

THe value of u is 0.

(4)The expression \frac{16}{3(\sqrt{2^{x}} )} is written as \frac{1}{3}(2^{4-\frac{x}{2}}).

\frac{16}{3(\sqrt{2^{x}} )}=\frac{2^4}{3(2^x)^{1/2}}\\\frac{16}{3(\sqrt{2^{x}} )}=\frac{1}{3}(2^{4-\frac{x}{2}})

The value of u is 4-\frac{x}{2}.

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