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Lesson Example Discussion Quiz: Class Homework

Step-3

Title: Find the value of "x"

Grade: 8-a Lesson: S3-L3

Explanation: Hello Students, time to practice and review the steps for the problem.

Lesson Steps

Step	Type	Explanation	Answer
1	Problem	Given that \$ 2^(3x+2) - 2^(3x-2) = 30\$
2	Formula:	Use law of exponents	\$a^(m-n) = a^m/a^n\$
3	Formula:	Use law of exponents	\$a^(m+n) = a^m * a^n\$
4	Step	After simplification	\$ 2^(3x) * 2^2 - 2^(3x)/2^2 = 30 \$
5	Hint	Take the common factor \$2^(3x)\$ for L.H.S	\$ 2^(3x)(4 - 1/4) = 30 \$
6	Step	After simplification we get	\$ 2^(3x)(15/4) = 30 \$
7	Step	Do the cross multiplication	\$ 15 * 2^(3x) = 120 \$
8	Step	move '15' to R.H.S and divide with '120'	\$ 2^(3x) = \cancel120^8/\cancel15 \$
9	Step	After cancellation we get	\$ 2^(3x) = 8 \$
10	Step	Equating both side bases	\$ 2^(3x) = 2^3 \$
11	Step	Here,both side base are equal so their powers also equal	\$ 3x = 3 \$
12	Step	After simplification	\$ x = \cancel3^1/\cancel3^1 \$
13	Step	After cancellation	\$x = 1\$
14		Answer	C

Step

Type

Explanation

Answer

Problem

Given that
\$ 2^(3x+2) - 2^(3x-2) = 30\$

Formula:

Use law of exponents

\$a^(m-n) = a^m/a^n\$

Formula:

Use law of exponents

\$a^(m+n) = a^m * a^n\$

Step

After simplification

\$ 2^(3x) * 2^2 - 2^(3x)/2^2 = 30 \$

Hint

Take the common factor \$2^(3x)\$ for L.H.S

\$ 2^(3x)(4 - 1/4) = 30 \$

Step

After simplification we get

\$ 2^(3x)(15/4) = 30 \$

Step

Do the cross multiplication

\$ 15 * 2^(3x) = 120 \$

Step

move '15' to R.H.S and divide with '120'

\$ 2^(3x) = \cancel120^8/\cancel15 \$

Step

After cancellation we get

\$ 2^(3x) = 8 \$

Step

Equating both side bases

\$ 2^(3x) = 2^3 \$

Step

Here,both side base are equal so their powers also equal

\$ 3x = 3 \$

Step

After simplification

\$ x = \cancel3^1/\cancel3^1 \$

Step

After cancellation

\$x = 1\$

Answer