Question

exponential and logarithmic functions
progress:
the movement of the progress bar may be uneven because questions can be worth more or less (including zero) de
solve: $8 = \log_{b}(256)$
$b = $
the solution is

Explanation:

Step1: Convert log to exponential form

By the definition of logarithms, if $\log_b(x) = y$, then $b^y = x$. Applying this gives:
$$b^8 = 256$$

Step2: Express 256 as power of 2

Rewrite 256 as an exponential term with base 2:
$$256 = 2^8$$

Step3: Equate bases and solve for b

Set the two expressions equal:
$$b^8 = 2^8$$
Since the exponents are equal and positive, the bases are equal:
$$b = 2$$

Answer:

$b=2$
The solution is $\boldsymbol{2}$