Final answer:
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