Question

What is the solution to this equation 2(1/49)^x-2=14

Answer 1

To solve the equation 2(1/49)^x-2=14, we can rearrange the equation and use logarithms to solve for x.

Step-by-step explanation:

To solve the equation 2(1/49)^x-2=14, we can start by rearranging the equation:

2(1/49)^x-2 = 14

2(1/49)^x = 14+2

2(1/49)^x = 16

(1/49)^x = 8

Now, we can take the logarithm of both sides to solve for x. Let's use the natural logarithm (ln):

ln((1/49)^x) = ln(8)

xln(1/49) = ln(8)

x = ln(8)/ln(1/49)

Using a calculator, we can find that x is approximately -2.102