Use the properties of logarithms to solve.
-
A) 2
B) 24
C) 7
D) 6

Question

Use the properties of logarithms to solve.
-
A) 2 
B) 24 
C) 7 
D) 6

Quizplus · Accepted Answer

Using the properties of logarithms, we can simplify the given expression as:

log(base 2)(x) + log(base 2)(2x+5) - log(base 2)(5x-1)

= log(base 2)((x)(2x+5)/(5x-1))

We need to find the value of x such that the expression simplifies to 6. That is,

log(base 2)((x)(2x+5)/(5x-1)) = 6

Using the definition of logarithm, we can write:

2^6 = (x)(2x+5)/(5x-1)

64(5x-1) = x(2x+5)

Expanding the expression on the right and simplifying, we get:

10x^2 - x - 320 = 0

Using the quadratic formula, we can solve for x:

x = [1 ± sqrt(1 + 4(10)(320))]/20

Since x cannot be negative, we take the positive value:

x = [1 + sqrt(12801)]/20 ≈ 6.27

Therefore, the answer is D) 6.

Use the Properties of Logarithms to Solve