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

Answer 1

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 = 3

Add 1:

3x = 4

Divide 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 = 49

Divide:

1 = 49/(7x * x)

Reformat:

1 = (72 - x)/x

Divide:

1/49 = 7-x/x

Reformat 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).