Exponential and Logarithmic Equations - IB DP Mathematics AA SL - Past Papers

Solve $5^{3y} = 2^{y+4}$, writing your answer in terms of $\ln 2$ and $\ln 5$.

Solve for $y$:
a $e^{3y} = 3e^y$
b $e^y = e^{-2y}$

Solve for $y$, giving an exact answer:
a $e^y = 15$
b $e^y = 2000$
c $3e^y = 0.5$

The lean body mass, $L$, in kilograms, of basketball players as a function of their age, $x$, in years, can be described by the logarithmic function:
$$L(x) = 8 \log(x - 14) + 45, \quad 17 \leq x \leq 26.$$
Determine the lean body mass for players aged:
(i) 17 years
(ii) 26 years.