Answered

Discover answers to your questions with Westonci.ca, the leading Q&A platform that connects you with knowledgeable experts. Get quick and reliable solutions to your questions from a community of experienced professionals on our platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

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
We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.