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Step-4

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 \$ 5^(x+2) - 5^(x-2) = 624\$
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	\$ 5^x*5^2 - 5^x/5^2 = 624 \$
5	Hint	Take the common factor \$5^x\$ for L.H.S	\$ 5^x(25 - 1/25) = 624 \$
6	Step	After simplification we get	\$ 5^x(624/25) = 624 \$
7	Step	Do the cross multiplication	\$ 624 * 5^x = 15600 \$
8	Step	move '624' to R.H.S and divide with '15600'	\$ 5^x= \cancel15600^25/\cancel624^1 \$
9	Step	After cancellation we get	\$ 5^x = 25 \$
10	Step	Equating both side bases	\$ 5^x = 5^2 \$
11	Step	Here,both side base are equal so their powers also equal	\$ x = 2 \$
12		Answer	B

Step

Type

Explanation

Answer

Problem

Given that
\$ 5^(x+2) - 5^(x-2) = 624\$

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

\$ 5^x*5^2 - 5^x/5^2 = 624 \$

Hint

Take the common factor \$5^x\$ for L.H.S

\$ 5^x(25 - 1/25) = 624 \$

Step

After simplification we get

\$ 5^x(624/25) = 624 \$

Step

Do the cross multiplication

\$ 624 * 5^x = 15600 \$

Step

move '624' to R.H.S and divide with '15600'

\$ 5^x= \cancel15600^25/\cancel624^1 \$

Step

After cancellation we get

\$ 5^x = 25 \$

Step

Equating both side bases

\$ 5^x = 5^2 \$

Step

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

\$ x = 2 \$

Answer