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Step-1

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\$'	\$ (3/2)^((3x)/2 - 5) = (3/2)^(1/9) \$
2	If Bases are equal powers also equal	\$ (3x)/2 - 5 = 1/9 \$
3	Taking LCM as '\$2\$'	\$ (3x - 10)/2 = 1/9 \$
4	By Cross Multiplication	\$9(3x - 10) = 2 \$ \$ 27x - 90 = 2 \$
5	Move constants to right side	\$ 27x = 2 + 90 \$ \$ 27x = 92 \$
6	Dividing on both sides by '\$27\$' of the equality	\$ (\cancel(27)x)/\cancel(27) = 92/27 \$
7	After Cancellation	\$ x = 92/27 \$
8	Answer	A = \$ x = 92/27 \$

Steps

Problem

Solution

Find the value of '\$x\$'

\$ (3/2)^((3x)/2 - 5) = (3/2)^(1/9) \$

If Bases are equal powers also equal

\$ (3x)/2 - 5 = 1/9 \$

Taking LCM as '\$2\$'

\$ (3x - 10)/2 = 1/9 \$

By Cross Multiplication

\$9(3x - 10) = 2 \$

\$ 27x - 90 = 2 \$

Move constants to right side

\$ 27x = 2 + 90 \$

\$ 27x = 92 \$

Dividing on both sides by '\$27\$' of the equality

\$ (\cancel(27)x)/\cancel(27) = 92/27 \$

After Cancellation

\$ x = 92/27 \$

Answer

A = \$ x = 92/27 \$