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svetlana [45]
3 years ago
5

25 POINTS! Which equation is equivalent to (1/3)=27^x^+^2

Mathematics
2 answers:
GenaCL600 [577]3 years ago
8 0

Answer:

match bases

remeber if a^b=a^c where a=a then b=c

remember

(x^m)^n=x^(mn)

1/(x^m)=x^-m

base of 3

(1/3)^x=(3^-1)^x=3^(-x)

27^(x+2)=(3^3)^(x+2)=3^(3x+6)

3^(-x)=3^(3x+6)

-x=3x+6

0=4x+6

-6=4x

-3/2=x

Genrish500 [490]3 years ago
7 0
Hint:     \bf  log_{{  a}}{{  b}}=y \iff {{  a}}^y={{  b}}
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Step-by-step explanation:

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Use the equation and type the ordered-pairs. y = log 3 x {(1/3, a0), (1, a1), (3, a2), (9, a3), (27, a4), (81, a5)
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Considering the given equation y = log_{3}x\\

And the ordered pairs in the format (x, y)

I don't know if it is log of base 3 or 10, but I will assume it is 3.

For (\frac{1}{3}, a_{0} )

x=\frac{1}{3}

y=a_{0}

y = log_{3}x\\y = log_{3}(\frac{1}{3} )\\y=-\log _3\left(3\right)\\y=-1

So the ordered pair will be (\frac{1}{3}, -1 )

For (1, a_{1} )

x=1

y=a_{1}

y = log_{3}x\\y = log_{3}1\\y = log_{3}(1)\\Note: \log _a(1)=0\\y = 0

So the ordered pair will be (1, 0 )

For (3, a_{2} )

x=3

y=a_{2}

y = log_{3}x\\y = log_{3}3\\y = 1

So the ordered pair will be (3, 1 )

For (9, a_{3} )

x=9

y=a_{3}

y = log_{3}x\\y = log_{3}9\\y=2\log _3\left(3\right)\\y=2

So the ordered pair will be (9, 2 )

For (27, a_{4} )

x=27

y=a_{4}

y = log_{3}x\\y = log_{3}27\\y=3\log _3\left(3\right)\\y=3

So the ordered pair will be (27, 3 )

For (81, a_{5} )

x=81

y=a_{5}

y = log_{3}x\\y = log_{3}81\\y=4\log _3\left(3\right)\\y=4

So the ordered pair will be (81, 4 )

4 0
3 years ago
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