May 2017

Solve for x if ln (x + 1) = 1 + ln x.

A bacterial culture is growing according to the formula y = 10,000e^0.6x where x is the time in days. Estimate the number of bacteria after one week.

A radioactive substance is decaying (it is changing into another element) according to the formula y = Ae^-0.2x where y is the amount of material remaining after x years. If the initial amount A = 80 grams, find the half life (time it takes for half of it to decompose) of this substance.

Solve for x if log_x (2x)^3x = 4x.

Solve for x if (x + 2) log_b b^x = x.

Solve for x if log₃ 2x - log₃ (x + 5) = 0.

Determine the value of x if log (x³ - 1) - log (x² + x + 1) = 1.

Solve for x if 2 log₂₅ x - log₂₅ (25 - 4x) = 1/2.

Solve for x if log₈ (x - 6) + log₈ (x + 6) = 2.

If $\log_x 2 = 1.2a$ and $\log_x 3 = 1.5a$, find $\log_x \sqrt{12}$ .