Solve for x 4^(7-3x)=1/16

Problem

4(7−3*x)=1/16

Solution

1. Rewrite the fraction on the right side as a power with a negative exponent.

1/16=16(−1)

2. Express both sides using the same base. Since 16=4 we can rewrite the right side in terms of base 4

16(−1)=(4)(−1)

3. Apply the power of a power rule (am)n=a(m*n) to simplify the right side.

(4)(−1)=4(−2)

4. Equate the exponents because the bases are now identical.

7−3*x=−2

5. Isolate the term containing x by subtracting 7 from both sides.

−3*x=−9

6. Solve for x by dividing both sides by −3

x=3

Final Answer

4(7−3*x)=1/16⇒x=3

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