Home > Precalculus > Logarithmic Models

How do you solve #log(x+3)-log(x-3)=2#?

Answer 1

Caleb Alexander

#x=101/33#

Use the identity #log(a)-log(b)=log(a/b)#.

#log(x+3)-log(x-3)=2#

#log(frac{x+3}{x-3})=2#

#frac{x+3}{x-3}=10^2=100#

#x+3=100(x-3)=100x-300#

#303=99x#

#x=303/99=101/33#

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Serenity Jones

To solve the equation (\log(x+3) - \log(x-3) = 2), we can use the properties of logarithms, specifically the quotient rule, which states that (\log(a) - \log(b) = \log\left(\frac{a}{b}\right)). Applying this rule to the given equation:

[\log\left(\frac{x+3}{x-3}\right) = 2]

Next, we can rewrite the equation in exponential form:

[10^2 = \frac{x+3}{x-3}]

Solving for (x), we have:

[100(x-3) = x+3]

[100x - 300 = x + 3]

[99x = 303]

[x = \frac{303}{99}]

[x = \frac{101}{33}]

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.