Respuesta :
You can use the definition of logarithms and some basic properties to find out the solution to the given equation.
The solution for Tenisha's system of equations is given approximately by x = -4.805
What is logarithm and some of its useful properties?
When you raise a number with an exponent, there comes a result.
Lets say you get
[tex]a^b = c[/tex]
Then, you can write 'b' in terms of 'a' and 'c' using logarithm as follows
[tex]b = log_a(c)[/tex]
Some properties of logarithm are:
[tex]log_a(b) = log_a(c) \implies b = c\\\\\log_a(b) + log_a(c) = log_a(b \times c)\\\\log_a(b) - log_a(c) = log_a(\frac{b}{c})\\\\log_a(b) + log_b(c) = log_a(c)[/tex]
Using the above property to evaluate the solution
The given equation is
[tex]log_3(5x) = log_5(2x + 8)[/tex]
Simplifying and using above properties, we get:
[tex]log_3(5x) = log_5(2x + 8)\\\\log_3(5) + log_3(x) = log_5(2) + log_5(x+4)\\\\\text{Adding}\: \rm log_5(3) \text{ on both the sides}\\\\log_5(3) + log_3(x) + log_3(5) = log_5(2) + log_5(x+4) + log_5(3)\\\\log_5(x) + log_3(5) - log_5(2) - log_5(3) = log_5(x+4)\\\\\text{Using the values of constant logs from calculator}\\\\\log_5(x) - log_5(x+4) = 1.11\\\\log_5(\dfrac{x}{x+4}) = 1.11\\\\\dfrac{x}{x+4} = 5^{1.11}\\\\x = 5.968 \times (x+4)\\4.968x = -23.872\\\\x \approx -4.805[/tex]
Thus,
The solution for Tenisha's system of equations is given approximately by x = -4.805
Learn more about logarithms here:
https://brainly.com/question/20835449
B) (1.0, 1.4)
I got it right on the quiz on Ed2020
Some other questions from the quiz and their answers (people will get different questions even on ed, but may have some in common if not all of them so im hoping this will help someone. )
Which system of equations could be graphed to solve the equation below? log Subscript 0.5 Baseline x = log Subscript 3 Baseline 2 + x
Answer: D
What is the approximate value of q in the equation below?
q+log26=2q+2
Answer: C (0.585)
Devonte used the change of base formula to approximate log Subscript 8 Baseline 25. Which expression did Devonte use?
Answer: D
Which system of equations could be graphed to solve the equation below? log (2 x + 1) = 3 x minus 2
Answer: B
Which expression can be used to approximate the expression below, for all positive numbers a, b, and x, where a Not-equals 1 and b Not-equals 1?
log Subscript x Baseline x
Answer: Not B lol I got it wrong
Which is equivalent to log Subscript 2 Baseline n = 4?
Answer: D
Tenisha solved the equation below by graphing a system of equations.
log Subscript 3 Baseline 5 x = log Subscript 5 Baseline (2 x + 8)
Answer: B
Consider the equation below.
log Subscript 4 Baseline (x + 3) = log Subscript 2 Baseline (2 + x) Which system of equations can represent the equation?
Answer: A
Which expression results when the change of base formula is applied to log Subscript 4 Baseline (x + 2)?
Answer: A
What is the approximate value of x in the equation below?
log Subscript 5 Baseline 15 = x + 3
Answer: B
