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Step-5

Title: Find the variable value

Grade: 7-b Lesson: S3-L10

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

Lesson Steps

Steps	Problem	Solution
1	Find the value of '\$x\$'	\$ (1/2)^(2x+4)=(1/4)^(3x + 15) \$
2	Applying identity '\$ 1/a^m = a^(-m) \$'	\$ (1/2)^(2x+4) = (1/2)^(2(3x + 15)) \$ \$ (1/2)^(2x+4) = (1/2)^(6x+30) \$
3	If Bases are equal powers also equal	\$ 2x+4 = 6x+30 \$
4	Move variables to the right side & constants to the left side	\$ 4 - 30 = 6x - 2x \$
5	After simplification	\$ -26 = 4x \$
6	Dividing on both sides by '\$3\$' of the equality	\$ (\cancel(4)x)/\cancel(4) = \cancel(-26)^13/\cancel(4)^2 \$
7	After Cancellation	\$ x = -13/2 \$
8	Answer	D = \$ x = -13/2 \$

Steps

Problem

Solution

Find the value of '\$x\$'

\$ (1/2)^(2x+4)=(1/4)^(3x + 15) \$

Applying identity '\$ 1/a^m = a^(-m) \$'

\$ (1/2)^(2x+4) = (1/2)^(2(3x + 15)) \$

\$ (1/2)^(2x+4) = (1/2)^(6x+30) \$

If Bases are equal powers also equal

\$ 2x+4 = 6x+30 \$

Move variables to the right side & constants to the left side

\$ 4 - 30 = 6x - 2x \$

After simplification

\$ -26 = 4x \$

Dividing on both sides by '\$3\$' of the equality

\$ (\cancel(4)x)/\cancel(4) = \cancel(-26)^13/\cancel(4)^2 \$

After Cancellation

\$ x = -13/2 \$

Answer

D = \$ x = -13/2 \$