Answered

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MATHEMATICS (21-30)

21. Solve the equation [tex]4^{c-1} = 64[/tex]

A. 1
B. 2
C. 3
D. 4

Sagot :

GinnyAnswer
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
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