Solve for x 1/16=64^(4x-3)

Problem

1/16=64(4*x−3)

Solution

1. Identify a common base for both sides of the equation. Since 16=4 and 64=4 we can use the base 4

2. Rewrite the left side using the property of negative exponents, where 1/(an)=a(−n)

1/16=1/4=4(−2)

3. Rewrite the right side by substituting 64 with 4 and applying the power of a power rule (am)n=a(m⋅n)

64(4*x−3)=(4)(4*x−3)=4(3*(4*x−3))

4. Equate the exponents since the bases are now the same.

−2=3*(4*x−3)

5. Distribute the 3 on the right side of the equation.

−2=12*x−9

6. Isolate the term containing x by adding 9 to both sides.

7=12*x

7. Solve for x by dividing both sides by 12

x=7/12

Final Answer

1/16=64(4*x−3)⇒x=7/12

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