Log Questions: Answers to x=2 & x=10^3

  • Thread starter Death
  • Start date
In summary, the conversation discusses two log problems and a question about the final answer. The first problem involves simplifying logarithmic expressions and solving for x, while the second problem involves solving a logarithmic equation. The conversation also includes a clarification on the steps taken to solve the second problem.
  • #1
Death
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I need some help on two log questions. I do understand everything of the problem until the final answer, it does not make sense.

Problem 1:
log3(x-1)^2 - log3(x^2 -1) = -1 + log3(x-1)

2log3(x-1) - log3(x^2 -1) = -1 + log3(x-1)

2log3(x-1) - log3(x-1) - log3(x^2 -1) = -1

log3(x-1) - log3(x^2 -1) = -1

log3 x-1/(x-1)(x+1) = -1

log3 1/x+1 = -1

=3^-1 = 1/3

x = 2 <=== why does it equal two?

Problem 2:
logx^5 + log x = (log x)(2logx)
5logx + logx = 2(logx)^2
6logx = 2(logx)^2
3 = logx <=== why does it equal 3? How does it turn from 6logx to 3?
x = 10^3

Thank you!
 
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  • #2
Originally posted by Death
I need some help on two log questions. I do understand everything of the problem until the final answer, it does not make sense.

Problem 1:
log3(x-1)^2 - log3(x^2 -1) = -1 + log3(x-1)

2log3(x-1) - log3(x^2 -1) = -1 + log3(x-1)

2log3(x-1) - log3(x-1) - log3(x^2 -1) = -1

log3(x-1) - log3(x^2 -1) = -1

log3 x-1/(x-1)(x+1) = -1

log3 1/x+1 = -1

=3^-1 = 1/3

x = 2 <=== why does it equal two?

Problem 2:
logx^5 + log x = (log x)(2logx)
5logx + logx = 2(logx)^2
6logx = 2(logx)^2
3 = logx <=== why does it equal 3? How does it turn from 6logx to 3?
x = 10^3

Thank you!

Problem 1
You got a little sloppy with parentheses

log3 x-1/(x-1)(x+1) = -1

log3 1/x+1 = -1

should be

log3 (x-1)/(x-1)(x+1) = -1

log3 1/(x+1) = -1

raise three to the power of each side yields

1/(x+1)=3^(-1)=1/3

1/(x+1)=1/3
x+1=3
x=2


Problem 2

6logx = 2(logx)^2
3 = logx <=== why does it equal 3? How does it turn from 6logx to 3?

both sides were divided by 2logx

6logx/2logx=3

2(logx)^2/2logx=logx

Njorl
 
  • #3
Thanks buddy.
 

What is the meaning of x=2?

The equation x=2 represents a linear function that has a slope of 0 and a y-intercept of 2. This means that for every value of x, the corresponding y-value will always be 2.

What is the significance of x=10^3?

The equation x=10^3 represents an exponential function with a base of 10 and an exponent of 3. This means that the value of x will increase by a factor of 10 for every unit increase in the exponent, resulting in a steep curve on a graph.

Can x=2 and x=10^3 coexist?

Yes, x=2 and x=10^3 can coexist as two separate equations with different values for x. However, if these equations are graphed together, they will not intersect since they represent different types of functions.

What is the solution to x=2 and x=10^3?

Since x=2 and x=10^3 represent two different equations, there is no single solution that satisfies both equations simultaneously. The solution to each equation will depend on the context and variables involved.

How can x=2 and x=10^3 be applied in real life?

The equations x=2 and x=10^3 can be applied in real life situations involving linear and exponential functions, respectively. For example, x=2 can represent a constant value, such as the cost of a small item, while x=10^3 can represent a rapidly growing quantity, such as the population of a city over time.

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