Answer :
To solve the equation \(4^{c-1} = 64\), let's follow these steps:
1. Express \(64\) as a power of \(4\):
Recognize that \(64\) can be written as a power of \(4\). We know that:
[tex]\[64 = 4^3\][/tex]
2. Rewrite the equation:
Substitute \(64\) with \(4^3\) in the original equation:
[tex]\[4^{c-1} = 4^3\][/tex]
3. Compare the exponents:
Since the bases are the same (both are \(4\)), we can set the exponents equal to each other:
[tex]\[c-1 = 3\][/tex]
4. Solve for \(c\):
To find \(c\), add \(1\) to both sides of the equation:
[tex]\[c - 1 + 1 = 3 + 1\][/tex]
[tex]\[c = 4\][/tex]
Thus, the solution to the equation \(4^{c-1} = 64\) is \(\boxed{4}\). Therefore, the correct answer is:
[d] 4
1. Express \(64\) as a power of \(4\):
Recognize that \(64\) can be written as a power of \(4\). We know that:
[tex]\[64 = 4^3\][/tex]
2. Rewrite the equation:
Substitute \(64\) with \(4^3\) in the original equation:
[tex]\[4^{c-1} = 4^3\][/tex]
3. Compare the exponents:
Since the bases are the same (both are \(4\)), we can set the exponents equal to each other:
[tex]\[c-1 = 3\][/tex]
4. Solve for \(c\):
To find \(c\), add \(1\) to both sides of the equation:
[tex]\[c - 1 + 1 = 3 + 1\][/tex]
[tex]\[c = 4\][/tex]
Thus, the solution to the equation \(4^{c-1} = 64\) is \(\boxed{4}\). Therefore, the correct answer is:
[d] 4
