Question

section 4.4 - properties of logarithms
question 18 of 19 (1 point) | question attempt: 1 of unlimited
(a) estimate the value of the logarithm between two consecutive integers.
4 < log₂20 < 5
part 2 of 3
(b) approximate the logarithm to 4 decimal places. if necessary, round intermediate steps to 9 decimal places.
log₂20 ≈ 4.3219
part: 2 / 3
part 3 of 3
(c) convert the result to exponential form.
the exponential form of log₂20 ≈ 4.3219 is □^□ ≈ □.

Explanation:

Step1: Recall the logarithmic - exponential relationship

If $y = \log_{a}x$, then $x=a^{y}$ (by the definition of logarithms: $\log_{a}x=y\Leftrightarrow a^{y}=x$).

Step2: Substitute the values of $a$, $y$, and $x$

Here, $a = 2$, $y=\log_{2}20\approx4.3219$, and $x = 20$.
So, using the formula $x=a^{y}$, we get $20\approx2^{4.3219}$.

Answer:

$2^{4.3219}\approx20$