Solve for t. (Round your answer to two decimal places.
(2 − (2.479/35))^7t= 29
take log of both sides
log [(2 − (2.479/35))^7t= 29] = log 29
7t log(2 − (2.479/35)) = log 29
7t(.2853...) = log 29
7t = log 29/.2853... = 5.1245...
t = .732078
= appr .73
check:
using 2 decimals
(2 − (2.479/35))^7t= 29.00000003 , not bad
To solve for t in the equation (2 − (2.479/35))^7t = 29, we need to isolate t by taking the logarithm of both sides. Let's go through the steps:
Step 1: Rewrite the equation:
(2 − (2.479/35))^7t = 29
Step 2: Take the logarithm of both sides. You can use any logarithm base you prefer; commonly used bases are 10 (log) and e (ln). For this example, we will use the natural logarithm (ln):
ln((2 − (2.479/35))^7t) = ln(29)
Step 3: Apply the logarithm property, which states that the logarithm of a number raised to an exponent can be rewritten as the product of the exponent and the logarithm of the number:
7t * ln(2 − (2.479/35)) = ln(29)
Step 4: Divide both sides of the equation by 7 * ln(2 − (2.479/35)):
t = ln(29) / (7 * ln(2 − (2.479/35)))
Now we can use a calculator to compute the value of t by plugging in ln(29) / (7 * ln(2 − (2.479/35))). Round the final answer to two decimal places.