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
Here's how to solve the logarithmic equation: The given equation is log_9 4 + log_3 3^x = 3. Step 1: Simplify the second logarithmic term. Using the logarithm property log_b b^p = p: log_3 3^x = x The equation now becomes: log_9 4 + x = 3 Step 2: Isolate x. Subtract log_9 4 from both sides: x = 3 - log_9 4 Step 3: Simplify the term log_9 4. We can change the base of the logarithm. Since 9 = 3^2, we can rewrite log_9 4 using base 3. Using the property log_b^k A = (1)/(k) log_b A: log_9 4 = log_3^2 4 = (1)/(2) log_3 4 Now, use the property p log_b A = log_b A^p: (1)/(2) log_3 4 = log_3 4^1/2 = log_3 sqrt(4) = log_3 2 Step 4: Substitute the simplified term back into the equation for x. x = 3 - log_3 2 The exact solution for x is: x = 3 - log_3 2 That's 2 down. 3 left today — send the next one.