7 to the power of x-1 multiply 49x equals 343 find x.? - Answers

7x-1 * 49x = 343.Firstly, we know that 49 = 72. Therefore, 49x = 72x.7x-1 * 72x = 343.Now, using the law of exponents, we add the 2 exponents due to the same bases.73x - 1 = 343.343 is a power of 7, 73 (49 * 7 = 343), therefore:73x - 1 = 73.Logarithm base 7 on both sides, resulting in a simple algebra problem:3x - 1 = 3Add 1:3x = 4Divide by 3:x = 4/3.However, there can be a far more complex problem. If 49x was actually 49x. This becomes 72x, and multiplying to 7x - 1 gets 7x + 1 * x = 343. Divide by 7, yielding:7x * x = 49Divide:1 = 49/(7x * x)Reformat:1 = (72 - x)/xDivide:1/49 = 7-x/xReformat into exponential form:1/49 = 1/x * e-x*ln(7)Multiply by -ln(7):-ln(7)/49 = -ln(7)/x * e-x*ln(7).Lambert W-function:x = (W(49*ln(7)))/ln(7) = 1.7210013512... (rounded up).