Solving Exponential and Logarithmic Equations Quiz Review

Simplify the sum of logarithms into a single logarithm.

$$\frac{2}{5}\log_5\left(x\right)+6\left(\log_5\left(y\right)-\frac{1}{2}\log_5\left(z\right)\right)$$

If $$\log_c\left(4\right)\approx2.165$$ , $$\log_c\left(11\right)\approx3.781$$ , and $$\log_c\left(3\right)\approx1.763$$ what is the approximate value of $$\log_c\left(\frac{12}{11}\right)$$ ?

What is the approximate value of $$\log_4\left(64^{1500}\right)$$ ?

Determine the solution to the equation $$4^x-5\cdot2^x-10=14$$ .

A gasoline-powered lawn mower produces a sound of 98 decibels. An electric lawn mower produces a sound of 73 decibels. Which statement best describes the comparison between the two types of lawn mowers?

Two bacteria cultures are compared after a period of time.

The first is untreated, and the number of bacteria after t hours is given by the function $$B_1\left(t\right)=3850\left(1.08\right)^t$$ .

The second is treated with a supplement, and the number of bacteria after t hours is given by the function $$B_2\left(t\right)=6540\left(0.86\right)^t$$ .

Which statement best describes the two bacteria cultures?

Two bacteria cultures are compared after a period of time.

The first is untreated, and the number of bacteria after t hours is given by the function $$B_1\left(t\right)=3850\left(1.08\right)^t$$ .

The second is treated with a supplement, and the number of bacteria after t hours is given by the function $$B_2\left(t\right)=6540\left(0.86\right)^t$$ .

After how many hours will the two cultures have the same number of bacteria?

(round the number of hours to 2 decimal places)

Two bacteria cultures are compared after a period of time.

The first is untreated, and the number of bacteria after t hours is given by the function $$B_1\left(t\right)=3850\left(1.08\right)^t$$ .

The second is treated with a supplement, and the number of bacteria after t hours is given by the function $$B_2\left(t\right)=6540\left(0.86\right)^t$$ .

At the time when the cultures have the same population, what is that population (rounded to the nearest hundred)?