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Step-5

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 \$ 7^(x-1) + 7^(x+2) = 344 \$
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	\$ 7^x/7 + 7^x * 7^2 = 344 \$
5	Hint	Take the common factor \$7^x\$ for L.H.S	\$ 7^x(1/7 + 49) = 344 \$
6	Step	After simplification we get	\$ 7^x(344/7) = 344 \$
7	Step	Do the cross multiplication	\$ 344 * 7^x = 2408 \$
8	Step	move '344' to R.H.S and divide with '2408'	\$ 7^x= \cancel2408^7/\cancel344 \$
9	Step	After cancellation we get	\$ 7^x = 7 \$
10	Step	Equating both side bases	\$ 7^x = 7^1 \$
11	Step	Here,both side base are equal so their powers also equal	\$ x = 1\$
12		Answer	C

Step

Type

Explanation

Answer

Problem

Given that
\$ 7^(x-1) + 7^(x+2) = 344 \$

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

\$ 7^x/7 + 7^x * 7^2 = 344 \$

Hint

Take the common factor \$7^x\$ for L.H.S

\$ 7^x(1/7 + 49) = 344 \$

Step

After simplification we get

\$ 7^x(344/7) = 344 \$

Step

Do the cross multiplication

\$ 344 * 7^x = 2408 \$

Step

move '344' to R.H.S and divide with '2408'

\$ 7^x= \cancel2408^7/\cancel344 \$

Step

After cancellation we get

\$ 7^x = 7 \$

Step

Equating both side bases

\$ 7^x = 7^1 \$

Step

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

\$ x = 1\$

Answer