# Math: log question-solving for x.

• shocklightnin
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.
shocklightnin

## Homework Statement

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

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?

Instead of doing all of that use this rule

logAa+logAb=logA(ab)

and then use the fact that logAa=n ⇒ a=An

https://www.physicsforums.com/attachment.php?attachmentid=22534&stc=1&d=1260947038
Try to understand each steps that i proceed.

#### Attachments

• 1.bmp
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Ah! I see now, thank you both so much!

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.

## 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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