Digital SATMath: AlgebraHard
A chemist is analyzing a solution whose pH level, P, is described by the equation P = -log(H+), where H+ is the hydrogen ion concentration. If the pH level of the solution is 3, what is the hydrogen ion concentration, H+?
- A0.01
- B0.1
- C1
- D0.001
Show answer & explanationAnswer & explanation
Correct answer: D. 0.001
Given P = -log(H+) and P = 3. So, 3 = -log(H+). Multiply by -1: -3 = log(H+). Since 'log' without a base specified implies base 10, this can be rewritten in exponential form as H+ = 10^(-3). This evaluates to H+ = 0.001.
Why the other options are wrong
- A. This would be 10^-2, corresponding to a pH of 2. Incorrect.
- B. This would be 10^-1, corresponding to a pH of 1. Incorrect.
- C. This would be 10^0, corresponding to a pH of 0. Incorrect.
Logarithmic and Exponential Forms
A logarithm is the inverse operation to exponentiation. The equation log_b(y) = x is equivalent to b^x = y. Converting between these forms is crucial for solving logarithmic and exponential equations.
- log_b(y) = x means 'b raised to the power of x equals y'.
- If no base 'b' is specified for 'log', it is assumed to be base 10 (common logarithm).
- If 'ln' is used, the base is 'e' (natural logarithm).
Memory trick: Log is the Exponent: 'Base to the power of log equals the argument'.