source : edu-answer.com

## What is 3 In 3

0 in 6

In 18

O In 27

In 3SOLVINGSWhat is 3 ln 3 – ln 9 expressed as a single natural logarithm

Since ln (m^n) = n⋅ln (m) … natural logarithmic propertyWe can further simplify the expression 3 ln 33 In 3 = In (3^3)Therefore, 3 ln 3 – ln 9 = In (3^3) – In 9

Since ln(m/n) =ln(m) – ln(n) … natural logarithmic propertyWe can further simplify the expression In (3^3) – In 9In (3^3) – In 9 = In [(3^3)/(9)]= In (27/9)= In 3

Therefore, 3 ln 3 – ln 9 expressed as a single natural logarithm is In 3.

Common and Natural Logarithms – Explanation & Examples – Common and Natural Logarithms – Explanation & Examples. The logarithm of a number is the power or exponent by which another value must be raised to produce an equivalent value of the given number.. The concept of logarithms was introduced in the early 17th century by John Napier – a Scottish mathematician. Later, scientists, navigators, and engineers adopted the concept to performFree simplify calculator – simplify algebraic expressions step-by-stepFree logarithmic equation calculator – solve logarithmic equations step-by-step

Simplify ln – Simplify Calculator – Symbolab – Using a calculator, we can use common and natural logarithms to solve equations of the form a x = b, especially when b cannot be expressed as a n. Example: Solve the equations a) 6 x + 2 = 21 b) e 2x = 9. Solution: a) 6 x + 2 = 21 log 6 x + 2 = log 21 (x + 2) log 6 = log 21. b) e 3x = 9 ln e 3x = ln 9 3x ln e = ln 9 3x = ln 93.2. THE NATURAL LOGARITHM FUNCTION 139 There is a technical point here that needs to be made. We have shown that a =ln(b) is a solution to ea = b;howdoweknowit'sthe (only) solution? After all: the equation a2 =9,for example, has two solutions: a =3and a = 3.Andtheequationsin(a)=0has inﬁnitely many:The natural log of the reciprocal of x is the opposite of the ln of x. Example: ln(⅓)= -ln(3) Power Rule. ln(x y) = y * ln(x) The natural log of x raised to the power of y is y times the ln of x. Example: ln(5 2) = 2 * ln(5) Key Natural Log Properties. In addition to the four natural logarithm rules discussed above, there are also several ln

Logarithmic Equation Calculator – Symbolab – Ln of 0. The natural logarithm of zero is undefined: ln(0) is undefined. The limit near 0 of the natural logarithm of x, when x approaches zero, is minus infinity: Ln of 1. The natural logarithm of one is zero: ln(1) = 0. Ln of infinity. The limit of natural logarithm of infinity, when x approaches infinity is equal to infinity: lim ln(xIn this section we will introduce logarithm functions. We give the basic properties and graphs of logarithm functions. In addition, we discuss how to evaluate some basic logarithms including the use of the change of base formula. We will also discuss the common logarithm, log(x), and the natural logarithm, ln(x).if by "in" and 'inc" you mean "ln" and "lnc" then i believe i can help. when you add logarithms, that means you multiply what is inside of the ln. so first pull out the 3. 3(ln3+lnc) then multiply the three and the c from inside the logarithms. 3(ln(3c)) that should be your answer. or you can pull the three up and make it: ln(3c)^3