Define logarithms as indices, where 𝑎𝑥 = 𝑏 is equivalent to 𝑥 = log𝑎 (𝑏), and convert between both forms.

A marine biologist is studying the pH levels in different sections of a coral reef ecosystem. The relationship between hydrogen ion concentration \([\text{H}^+]\) (in moles per litre) and pH is given by the equation \(\text{pH} = -\log_{10}([\text{H}^+])\). Refer to the table below showing hydrogen ion concentrations measured at four reef locations. (a) Convert the pH equation into exponential form, expressing \([\text{H}^+]\) in terms of pH. [1 mark] (b) Calculate the pH value at Location B, correct to two decimal places. [1 mark] (c) At Location D, the measured pH is 7.85. Determine the hydrogen ion concentration \([\text{H}^+]\) at this location, expressing your answer in scientific notation correct to two significant figures. [2 marks]

Which of the following is equivalent to \(5^4 = 625\)?

A student writes the equation \( 3^5 = 243 \) on the board. (a) Define what a logarithm represents in terms of indices. (b) Convert the equation \( 3^5 = 243 \) into logarithmic form. (c) State the value of \( \log_3(243) \).