Question

3^x - 3^x-1= 18
A)3
B)8
c)27
D)216

Answer 1

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3^x - 3^x-1 = 18

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

3^x(1–1/3) = 18

3^x(2/3) = 18

3^x = 18X3/2

3^x = 27

Express 27 in terms of 3^something

3^x = 3^3

RHS and LHS have equal bases, so exponents will be equal,

ie x = 3

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Answer 2

$\: \: \: \: \: \: \: \: {3}^{x} - {3}^{x - 1} = 18 \\ = > {3}^{x}(1 - {3}^{ - 1}) = 6 \times 3 \\ = > {3}^{x}(1 - \frac{1}{3}) = 18 \\ = > { 3 }^{x} \times \frac{2}{3} = 18 \\ = > {3}^{x} = 18 \times \frac{3}{2} \\ = > {3}^{x} = 27 \\ = > {3}^{x} = {3}^{3}$
When bases are same,
Exponents will also be same.
=>x = 3.



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