Question

section 4.4 - properties of logarithms
question 19 of 19 (1 point) | question attempt: 1 of unlimited
part 2 of 3
(b) approximate the logarithm to 4 decimal places. if necessary, round intermediate steps to 9 decimal places.
log₃0.001 ≈ -6.2920
correct answer
-6.2877
part: 2 / 3
part 3 of 3
(c) convert the result to exponential form.
the exponential form of log₃0.001 ≈ -6.2877 is ≈.

Explanation:

Step1: Use the logarithmic - exponential conversion formula

The formula for converting a logarithmic equation $\log_{a}b = c$ to an exponential equation is $a^{c}=b$.

Step2: Substitute the values

Given $\log_{3}0.001\approx - 6.2877$, here $a = 3$, $c=-6.2877$, and $b = 0.001$.
By the formula $a^{c}=b$, we get $3^{-6.2877}\approx0.001$.

Answer:

$3^{-6.2877} \approx 0.001$