Question

lets investigate! find the missing values of x in the table given the equation below for y. use your knowledge of logarithms to help you! y = 3(10^x) click here when you think youve got it!

Explanation:

Step1: Rearrange the equation for x

Given $y = 3(10^{x})$, we can rewrite it as $10^{x}=\frac{y}{3}$. Then, using the definition of a logarithm ($y = a^{x}$ is equivalent to $x=\log_{a}y$), we have $x=\log_{10}(\frac{y}{3})=\log(\frac{y}{3})$.

Step2: Find x when y = 300

Substitute $y = 300$ into $x=\log(\frac{y}{3})$. So $x=\log(\frac{300}{3})=\log(100)$. Since $10^{2}=100$, then $x = 2$.

Step3: Find x when y = 1503.56

Substitute $y = 1503.56$ into $x=\log(\frac{y}{3})$. So $x=\log(\frac{1503.56}{3})=\log(501.1867)$. Using a calculator, $x\approx 2.7$.

Answer:

When $y = 300$, $x = 2$; when $y = 1503.56$, $x\approx 2.7$