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]
