Sure, let's solve the equation [tex]\(\log_2(z) = 9\)[/tex].
To begin, recall that a logarithm can be interpreted as the power to which the base must be raised to obtain the given number. In this equation, the base is [tex]\(2\)[/tex] and the result is [tex]\(z\)[/tex].
We start by converting the logarithmic equation into its exponential form. The general rule is:
[tex]\[
\log_b(a) = c \implies a = b^c
\][/tex]
In our specific equation, [tex]\(\log_2(z) = 9\)[/tex], this means:
[tex]\[
z = 2^9
\][/tex]
Next, we need to determine the value of [tex]\(2^9\)[/tex]. We do this by evaluating the power:
[tex]\[
2^9 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2
\][/tex]
Rather than multiply each factor step-by-step, we can recognize that:
[tex]\[
2^9 = 512
\][/tex]
Thus, the value of [tex]\(z\)[/tex] is:
[tex]\[
z = 512
\][/tex]
So, the solution to the equation [tex]\(\log_2(z) = 9\)[/tex] is:
[tex]\[
z = 512
\][/tex]
