Evaluate: log_(16)64 Answer:

Understand the problem: Understand the problem. We need to find the exponent to which 16 must be raised to get 64. Express as power of 16: Express 64 as a power of 16. Since 64 is 16 squared (16^2), we can write 64 as 16^2. Apply logarithm definition: Apply the definition of a logarithm. The logarithm log_base(b)(a) is the exponent x such that b^x = a. Here, we have 16^x = 64, and from Step 2, we know that 64 is 16^2. Therefore, x = 2. Conclude the solution: Conclude the solution. Since 16^2 = 64, log_(16)64 = 2.

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Evaluate: $\newline$ $\log _{16} 64$ $\newline$ Answer:

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Q. Evaluate:

\newline

\log _{16} 64

\newline

Answer:

Understand the problem: Understand the problem. We need to find the exponent to which $16$ must be raised to get $64$ .
Express as power of $16$ : Express $64$ as a power of $16$ . Since $64$ is $16$ squared ( $16^2$ ), we can write $64$ as $16^2$ .
Apply logarithm definition: Apply the definition of a logarithm. The logarithm $\log_{\text{base}}(b)(a)$ is the exponent $x$ such that $b^x = a$ . Here, we have $16^x = 64$ , and from Step $2$ , we know that $64$ is $16^2$ . Therefore, $x = 2$ .
Conclude the solution: Conclude the solution. Since $16^2 = 64$ , $\log_{16}64 = 2$ .