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Step-2

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\$'	\$ (2/3)^((4x+6)/2) = (3/2)^2 \$
2	Applying identity '\$ 1/a^m = a^(-m) \$'	\$ (2/3)^((4x+6)/2) = (2/3)^-2 \$
3	If Bases are equal powers also equal	\$ (4x+6)/2 = -2 \$
4	By Cross Multiplication	\$ 4x+6 = -4 \$
5	Move constants to the right side	\$ 4x = -4 - 6 \$ \$ 4x = -10 \$
6	Dividing on both sides by '\$4\$' of the equality	\$ (\cancel(4)x)/\cancel(4) = \cancel(-10)^5/\cancel(4)^2 \$
7	Answer	c = \$ x = -5/2 \$

Steps

Problem

Solution

Find the value of '\$x\$'

\$ (2/3)^((4x+6)/2) = (3/2)^2 \$

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

\$ (2/3)^((4x+6)/2) = (2/3)^-2 \$

If Bases are equal powers also equal

\$ (4x+6)/2 = -2 \$

By Cross Multiplication

\$ 4x+6 = -4 \$

Move constants to the right side

\$ 4x = -4 - 6 \$

\$ 4x = -10 \$

Dividing on both sides by '\$4\$' of the equality

\$ (\cancel(4)x)/\cancel(4) = \cancel(-10)^5/\cancel(4)^2 \$

Answer

c = \$ x = -5/2 \$