Question

${3}^{x} - {3}^{x - 1} = 18$
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Answer 1

Question:

Solve for "x" in the given equation;

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

Answer:

x = 3 .

Note:

• (x^a)•(x^b) = x^(a+b)

• (x^a)/(x^b) = x^(a-b)

• (x^a)^b = x^(a•b)

Solution:

We have;

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

=> 3^x - (3^x)/3 = 18

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

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

=> (3^x)(2/3) = 18

=> 3^x = 18•(3/2)

=> 3^x = 27

=> 3^x = 3^3

=> x = 3

Hence,

The required value of "x" is 3 .

Answer 2

Step-by-step explanation:

${3}^{x} - {3}^{x - 1} = 18 \\ {3}^{x} (1 - \frac{1}{3} ) = 18 \\ {3}^{x} \times \frac{2}{3} = 18 \\ {3}^{x} = 27 \\ {3}^{x} = {3}^{3} \\ \\ equating \: power \: since \: bases \: are \: equal \\ hence \: x = 3$