Question

question 2 of 10
what is the solution to the equation below? round your answer to two decimal places.
\\(\log_3 x = 2.2\\)
\\(\bigcirc\\) a. \\(x = 6.60\\)
\\(\bigcirc\\) b. \\(x = 10.65\\)
\\(\bigcirc\\) c. \\(x = 11.21\\)
\\(\bigcirc\\) d. \\(x = 9.03\\)

Explanation:

Step1: Convert logarithmic to exponential

Recall the definition of logarithms: if $\log_{b} a = c$, then $a = b^{c}$. So for $\log_{3} x = 2.2$, we can rewrite it as $x = 3^{2.2}$.

Step2: Calculate the value of $3^{2.2}$

Using a calculator, we know that $3^{2.2}=3^{2 + 0.2}=3^{2}\times3^{0.2}=9\times3^{0.2}$. Calculate $3^{0.2}\approx1.2457$, then $9\times1.2457\approx11.21$.

Answer:

C. $x = 11.21$