This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
You're on a roll — a) Step 1: Rewrite the square root as a fractional exponent. y = x^1/2 Step 2: Take the logarithm base 10 of both sides of the equation. _10 y = _10 (x^1/2) Step 3: Apply the power rule of logarithms, _b (M^c) = c _b M. _10 y = (1)/(2) _10 x The logarithmic equation is: _10 y = (1)/(2) _10 x b) Step 1: Take the logarithm base 10 of both sides of the equation. _10 y = _10 (120 × 3^x) Step 2: Apply the product rule of logarithms, _b (MN) = _b M + _b N, to the right side. _10 y = _10 120 + _10 (3^x) Step 3: Apply the power rule of logarithms, _b (M^c) = c _b M, to the term _10 (3^x). _10 y = _10 120 + x _10 3 The logarithmic equation is: _10 y = _10 120 + x _10 3 What's next?