Math: log question-solving for x.

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In summary, the conversation discusses solving an equation involving logarithms and the steps involved in finding a solution. The conversation also mentions a rule for logarithms and reminds the reader to consider the restrictions when solving the equation.
  • #1
shocklightnin
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Homework Statement


Solve: log(sub6)x+log(sub6)(x-5) = 2


Homework Equations



na?

The Attempt at a Solution



i multiplied the second log out and got:
log(sub6)x+log(sub6)x-log(sub6)5 = 2
then i put the x's on one side and the numbers on the other.
2(log(sub6)x) = 2+log(sub6)5

but i have no idea how to go from there. or maybe i multiplied it out wrong?
 
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  • #2
Instead of doing all of that use this rule

logAa+logAb=logA(ab)

and then use the fact that logAa=n ⇒ a=An
 
  • #3
https://www.physicsforums.com/attachment.php?attachmentid=22534&stc=1&d=1260947038
Try to understand each steps that i proceed.
 

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  • #4
Ah! I see now, thank you both so much!
 
  • #5
Remember that from your original equation x has to be positive and x has to be greater than 5 (which together mean that x > 5). Otherwise one of the terms in your original equation will be undefined.
 

Related to Math: log question-solving for x.

1. How do I solve for x in a logarithmic equation?

To solve for x in a logarithmic equation, you can use the properties of logarithms to rewrite the equation in a simpler form. Then, you can isolate x by applying the inverse operation of logarithms, which is exponentiation.

2. What is the difference between a logarithm and an exponent?

A logarithm is the inverse operation of an exponent. This means that a logarithm tells you what power (exponent) you need to raise a base to in order to get a certain number. For example, log2 8 = 3, which means 2 to the power of 3 equals 8.

3. Can I solve for x in a logarithmic equation without using a calculator?

Yes, you can solve for x in a logarithmic equation without using a calculator by using the properties of logarithms and basic algebraic techniques such as factoring and simplifying.

4. What are the common bases used in logarithmic equations?

The most common bases used in logarithmic equations are base 10 (log10 x), base e (ln x), and base 2 (log2 x). However, any positive number can be used as the base for a logarithm.

5. How can I check my solution for x in a logarithmic equation?

You can check your solution for x in a logarithmic equation by plugging in your solution into the original equation and making sure both sides are equal. You can also use a calculator to evaluate both sides of the equation and see if they are equal.

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