Quick questions on Exponentials and logarithms: laws, equations and modelling - WJEC A-Level Maths

An exponential function $y = a^x$ (with $a > 0$) passes through $(0, 1)$, is always positive, and increases for $a > 1$ or decreases for $0 < a < 1$. The special base $\mathrm{e} \approx 2.71828$ gives the natural exponential $\mathrm{e}^x$, which has the property that its gradient equals its value, central to the calculus that follows.

A relationship of the form $y = k a^x$ becomes linear when you take logarithms: $\log y = \log k + x\log a$. Plotting $\log y$ (vertical) against $x$ (horizontal) gives a straight line with gradient $\log a$ and vertical intercept $\log k$, so you can recover the constants from a fitted line.

Write $2\log x - \log 3$ as a single logarithm. [2 marks]

Solve $\ln(2x + 1) = 3$, giving $x$ to three significant figures. [3 marks]

A quantity satisfies $y = 4 \times 3^x$. Find $x$ when $y = 36$. [2 marks]