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Solve the exponential equation.
1/16=64^4x−3
To solve the exponential equation 1/16 = 64^(4x-3), we can rewrite both sides using exponential notation with the same base.
1/16 = (2^6)^(4x-3)
Since we have an exponent raised to another exponent, we can apply the exponent rule which states that when you raise an exponent to another exponent, you multiply the exponents.
1/16 = 2^(6(4x-3))
Simplifying further,
1/16 = 2^(24x-18)
To get rid of the fraction on the left side, we can write 1/16 as 2^(-4) using the exponent rule that states a^(-b) = 1/a^b.
2^(-4) = 2^(24x-18)
Since the bases on both sides are the same, we can set the exponents equal to each other.
-4 = 24x-18
To solve for x, we can start by adding 18 to both sides.
-4 + 18 = 24x
14 = 24x
Finally, to isolate x, we can divide both sides by 24.
14/24 = x
7/12 = x
Therefore, the solution to the exponential equation is x = 7/12.