Question

704869(1+0.87)^x=4000000(1-0.013)^×

Answer 1

To solve the given equation, we need to get rid of the parentheses first.

So, we have:

704869(1+0.87)^x = 4000000(1-0.013)^x

Simplify the expression:

704869 * 1.87^x = 4000000 * 0.987^x

Divide both sides by 704869:

1.87^x = (4000000 * 0.987^x) / 704869

Divide 4000000 by 704869:

1.87^x = 5.67133 * 0.987^x

Now, take natural logarithm on both sides to solve for x:

ln(1.87^x) = ln(5.67133 * 0.987^x)

Using the property of logarithms, we get:

x * ln(1.87) = ln(5.67133) + x * ln(0.987)

Subtract x * ln(0.987) from both sides:

x * ln(1.87) - x * ln(0.987) = ln(5.67133)

Factor out x:

x(ln(1.87) - ln(0.987)) = ln(5.67133)

Now, divide both sides by (ln(1.87) - ln(0.987)) to solve for x:

x = ln(5.67133) / (ln(1.87) - ln(0.987))

Calculating the values:

x ≈ 32.21

Therefore, the value of x is approximately 32.21.