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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 \$ 4^(x-1) + 4^(x+1) = 272 \$
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 we get	\$ 4^x/4 + 4^x * 4 = 272 \$
5	Hint	Take the common factor \$4^x\$ for L.H.S	\$ 4^x(1/4 + 4) = 272 \$
6	Step	After simplification we get	\$ 4^x(17/4) = 272 \$
7	Step	Do the cross multiplication	\$ 17 * 4^x = 1088 \$
8	Step	move '17' to R.H.S and divide with '1088'	\$ 4^x= \cancel1088^64/\cancel17^1 \$
9	Step	After cancellation we get	\$ 4^x = 64 \$
10	Step	Equating both side bases	\$ 4^x = 4^3 \$
11	Step	Here,both side base are equal so their powers also equal	\$ x = 3 \$
12		Answer	C

Step

Type

Explanation

Answer

Problem

Given that
\$ 4^(x-1) + 4^(x+1) = 272 \$

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 we get

\$ 4^x/4 + 4^x * 4 = 272 \$

Hint

Take the common factor \$4^x\$ for L.H.S

\$ 4^x(1/4 + 4) = 272 \$

Step

After simplification we get

\$ 4^x(17/4) = 272 \$

Step

Do the cross multiplication

\$ 17 * 4^x = 1088 \$

Step

move '17' to R.H.S and divide with '1088'

\$ 4^x= \cancel1088^64/\cancel17^1 \$

Step

After cancellation we get

\$ 4^x = 64 \$

Step

Equating both side bases

\$ 4^x = 4^3 \$

Step

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

\$ x = 3 \$

Answer