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
Welcome back kiendeperuse — been a while! Let's pick up where you left off. To express an exponential equation b^x = y in logarithmic notation, we use the form _b y = x. e) Given the equation 5^0 = 1. Step 1: Identify the base, exponent, and result. Here, the base b=5, the exponent x=0, and the result y=1. Step 2: Convert to logarithmic notation. Using the rule _b y = x, we get: _5 1 = 0 The student's attempt 5 = 1 is incorrect because it implies 10^1 = 5, which is false. The correct base for the logarithm should be 5, and the result of the logarithm is the exponent, 0. The final answer is _5 1 = 0. g) Given the equation 125 = ((1)/(5))^-3. Step 1: Identify the base, exponent, and result from the exponential form. Here, the base b=(1)/(5), the exponent x=-3, and the result y=125. Step 2: Convert to logarithmic notation. Using the rule _b y = x, we get: _(1)/(5) 125 = -3 The final answer is _(1)/(5) 125 = -3. Send me the next one 📸