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 — Here's the solution for question 3. a): 3. a) Find the value of x in the equation 49^x+1 + 7^2x = 350. Step 1: Rewrite the equation with a common base. The base 49 can be written as 7^2. (7^2)^x+1 + 7^2x = 350 Apply the exponent rule (a^m)^n = a^mn: 7^2(x+1) + 7^2x = 350 7^2x+2 + 7^2x = 350 Step 2: Use the exponent rule a^m+n = a^m · a^n. 7^2x · 7^2 + 7^2x = 350 Calculate 7^2: 49 · 7^2x + 7^2x = 350 Step 3: Factor out the common term 7^2x. 7^2x(49 + 1) = 350 7^2x(50) = 350 Step 4: Isolate the exponential term 7^2x. 7^2x = (350)/(50) 7^2x = 7 Step 5: Equate the exponents. Since 7 = 7^1, we can equate the exponents: 2x = 1 x = (1)/(2) The value of x is (1)/(2). What's next?