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Identify the values of [tex]\(a\)[/tex], [tex]\(b\)[/tex], and [tex]\(c\)[/tex] that make the statement below true:

[tex]\[
\log_2 64 = 6 \quad \text{if and only if} \quad a^b = c
\][/tex]

[tex]\[
a = \square
\][/tex]

[tex]\[
b = \square
\][/tex]

[tex]\[
c = \square
\][/tex]

Sagot :

GinnyAnswer
Sure, let's solve the equation step by step.

We are given:
[tex]\[ \log_2(64) = 6 \][/tex]

This equation can be read as follows: "The logarithm base 2 of 64 equals 6."

To translate this into an exponential equation, we interpret it to mean:
[tex]\[ 2^6 = 64 \][/tex]

In this form, the base is 2, the exponent is 6, and the result is 64.

So, we can identify the values of [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex] as follows:
[tex]\[ a = 2 \][/tex]
[tex]\[ b = 6 \][/tex]
[tex]\[ c = 64 \][/tex]

These values satisfy the given logarithmic equation when converted to its exponential form. Thus, the solution is:
[tex]\[ a = 2 \][/tex]
[tex]\[ b = 6 \][/tex]
[tex]\[ c = 64 \][/tex]
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