Question

7(1.02^x)=14(1.03^x)
x=

Answer 1

23.44 (Please RECHECK ANSWER)!!!!!

Explanation:

To solve this equation for x, we can start by dividing both sides by 7:

1.02^x = 2(1.03^x)

Next, we can take the natural logarithm (ln) of both sides:

ln(1.02^x) = ln(2(1.03^x))

Using the logarithmic property that ln(ab) = ln(a) + ln(b), we can simplify the right side of the equation:

ln(1.02^x) = ln(2) + ln(1.03^x)

Now we can use the power rule of logarithms that ln(a^b) = b ln(a) to simplify the left side of the equation:

x ln(1.02) = ln(2) + x ln(1.03)

Taking the x terms to one side and factoring out x, we get:

x(ln(1.02) - ln(1.03)) = ln(2)

Dividing both sides by (ln(1.02) - ln(1.03)), we get:

x = ln(2) / (ln(1.02) - ln(1.03))

Using a calculator, we can solve for x:

x = 23.44 (rounded to two decimal places)

Therefore, x is approximately 23.44.