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If 3^(x)-3^(x-1)=18 the value of 2^x is?

Answer 1

Benjamin Achtenberg

# 8#.

#3^x-3^(x-1)=18#.

#:. 3^x-3^x/3^1=18#.

#:. 3^x(1-1/3)=18#.

#:. 3^x*2/3=18#.

#:. 3^x=18*3/2=27=3^3#.

#:. x=3#.

# rArr 2^x=2^3=8#.

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Answer 2

Sadie Alexander

To find the value of ( 2^x ), we first solve the equation ( 3^x - 3^{x-1} = 18 ) for ( x ):

[ 3^x - 3^{x-1} = 18 ]

[ 3^x - \frac{3^x}{3} = 18 ]

[ 3^x - \frac{1}{3} \times 3^x = 18 ]

[ \frac{2}{3} \times 3^x = 18 ]

[ 3^x = \frac{18 \times 3}{2} ]

[ 3^x = 27 ]

[ x = \log_3(27) ]

[ x = 3 ]

Now that we have found the value of ( x ), we can find the value of ( 2^x ):

[ 2^x = 2^3 ]

[ 2^x = 8 ]

So, the value of ( 2^x ) is ( 8 ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.