Question

Grade 7 IIT Foundation Maths.
Answer step by step.
${3}^{a} - {3}^{a - 1} = 18$
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Answer 1

$\Large\text{\underline{\underline{Question}}}$

Solve the following equation: -

$\text{ \cdots\longrightarrow\boxed{3^{a}-3^{a-1}=18.} }$

$\Large\text{\underline{\underline{Related topic}}}$

Exponential properties

We use exponents as a way to treat either huge or tiny numbers. In the scientistic notation, astronomy, and more. Some say, in a joke, that the life expectancy of astronomers doubled after the development of exponents and logarithms.

Some crucial exponential properties

$\text{ \cdots\longrightarrow\boxed{a^{m}\cdot a^{n}=a^{m+n}.} }$

$\text{ \cdots\longrightarrow\boxed{a^{m}\div a^{n}=a^{m-n}.} }$

$\Large\text{\underline{\underline{Explanation}}}$

Let's multiply 3 on both equations.

$\cdots\longrightarrow3^{a+1}-3^{a}=2\cdot3^{3}.$

Now, we can find the common factor on the left-hand side.

$\cdots\longrightarrow3^{a}\cdot(3-1)=2\cdot3^{3}.$

Let's divide by 2.

$\cdots\longrightarrow3^{a}=3^{3}.$

Now, we can solve the equation by comparing the exponents.

$\cdots\longrightarrow\boxed{a=3.}$

$\Large\text{\underline{\underline{More information}}}$

Some other properties of exponents

$\text{ \cdots\longrightarrow \boxed{a^{-n}=\dfrac{1}{a^{n}}. \ (a\neq0.)} }$

$\text{ \cdots\longrightarrow \boxed{a^{0}=1. \ (a\neq0.)} }$

$\text{ \cdots\longrightarrow \boxed{(a^{m})^{n}=a^{mn}.} }$

$\text{ \cdots\longrightarrow \boxed{\sqrt[n]{a}=a^{\frac{1}{n}}.} }$

Answer 2

Step-by-step explanation:

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

3^a - 3^a /3 =18

3^a ( 1- 1/3)=18

3^a (2/3) = 18

3^a = 18× 3/2

3^a = 27

3^a = 3^3

a = 3

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