Solve for x 1.2^x=(0.5)^(-x)

Problem

1.2=(0.5)(−x)

Solution

1. Apply the negative exponent rule to the right side of the equation to simplify the base.

(0.5)(−x)=(1/0.5)x

2. Simplify the base on the right side by calculating the reciprocal of 0.5

1/0.5=2

3. Rewrite the equation using the simplified base.

1.2=2

4. Divide both sides by 2 to group the terms with the exponent x on one side.

1.2/2=1

5. Apply the power of a quotient rule to combine the bases under a single exponent.

(1.2/2)x=1

6. Simplify the fraction inside the parentheses.

0.6=1

7. Apply the zero exponent property, which states that any non-zero base raised to the power of 0 equals 1

x=0

Final Answer

1.2=(0.5)(−x)⇒x=0

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