Calculus questions Solve the following equation for x. Remember, do not leave ne

Question

Calculus questions

Solve the following equation for x. Remember, do not leave negative exponents. 3 + ln x = 0 Solve the following equation for x: 2 -ln (x + 3 ) = ln 4 Differentiate the following function. Note: This is slightly challenging. (ln (x2 + 2)) Find the slope of the graph of y = ln (2x + 3)1 / 2 when x = 3. Expand the following expression to be a sum or difference of logarithms such that no variable is raised to any power (other than the power of one, obviously): ln x5 y-4 / w3 z-2 A certain radioactive substance is decaying at a rate proportional to the amount present. If 100 grams decays to 13.5 grams in 4 years, how many years will it take for 90 grams to decay to 30 grams? Round your answer to three decimal places.

Explanation / Answer

do not post all questions in one post.it is against chegg's rule.

i'll solve only two of them for you.

7)

3 + ln(x) = 0

ln(x) = -3

x = e^(-3) = 0.04978706836786

8)

2 - ln(x+3) = ln4

2 = ln(x+3) + ln4

2 = ln(4x + 12)

4x +12 = e^2

x = [e^2 - 12]/4 = -1.1527359

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