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Lesson Example Discussion Quiz: Class Homework

Step-1

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 \$ 3^(2x-1) + 3^(2x+1) = 270\$
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	\$ 3^(2x)/3 + 3^(2x) * 3 = 270 \$
5	Hint	Take the common factor \$3^(2x)\$ for L.H.S	\$ 3^(2x)(1/3 + 3) = 270 \$
6	Step	After simplification we get	\$ 3^(2x)(10/3) = 270 \$
7	Step	Do the cross multiplication	\$ 10 * 3^(2x) = 810 \$
8	Step	move '10' to R.H.S and divide with '810'	\$ ( 3^(2x))= \cancel810^81/\cancel10 \$
9	Step	After cancellation we get	\$ 3^(2x) = 81 \$
10	Step	Equating both side bases	\$ 3^(2x) = 3^4 \$
11	Step	Here,both side base are equal so their powers also equal	\$ 2x = 4 \$
12	Step	After simplification	\$ x = \cancel4^2/\cancel2^1\$
13	Step	After cancellation	\$x = 2\$
14		Answer	A

Step

Type

Explanation

Answer

Problem

Given that
\$ 3^(2x-1) + 3^(2x+1) = 270\$

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

\$ 3^(2x)/3 + 3^(2x) * 3 = 270 \$

Hint

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

\$ 3^(2x)(1/3 + 3) = 270 \$

Step

After simplification we get

\$ 3^(2x)(10/3) = 270 \$

Step

Do the cross multiplication

\$ 10 * 3^(2x) = 810 \$

Step

move '10' to R.H.S and divide with '810'

\$ ( 3^(2x))= \cancel810^81/\cancel10 \$

Step

After cancellation we get

\$ 3^(2x) = 81 \$

Step

Equating both side bases

\$ 3^(2x) = 3^4 \$

Step

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

\$ 2x = 4 \$

Step

After simplification

\$ x = \cancel4^2/\cancel2^1\$

Step

After cancellation

\$x = 2\$

Answer