107. Evaluate: logx 16 = -2
a. 0.25
b. 4
c. -4
d. -0.25
108. Evaluate: e2 ln 3
a. 6
b. 9
c. 12
d. 18
107. Solve
log_x 16 = -2
16 = x^-2
16 = 1/x^2
x = 1/4
108.
e^(2 ln 3)
(e^ln 3)^2
3^2
9
thaanks ;3
To evaluate logarithmic and exponential expressions, we need to remember the properties of logarithms and exponentials.
For question 107:
We are given the equation logx 16 = -2. This equation represents the logarithmic form of x^(-2) = 16. In other words, x raised to the power of -2 equals 16.
To solve for x, we can rewrite this equation in exponential form. Taking the reciprocal of both sides gives us x^2 = 1/16. Now, we can take the square root of both sides to find x.
√(x^2) = ±√(1/16)
Since we are only interested in the positive square root, we have x = 1/4 or x = -1/4.
So, the correct answer for question 107 is option a. 0.25.
For question 108:
We are asked to evaluate e^(2 ln 3). Here, we need to apply the property of logarithms that states ln(a^b) = b ln(a). Using this property, we can rewrite the expression as e^(ln 3^2).
Since e and ln are inverse functions, e^(ln x) = x. Therefore, e^(ln 3^2) = 3^2 = 9.
So, the correct answer for question 108 is option b. 9.