# Help with logarithms pls

• Nx2
In summary, the conversation is about a student seeking help with solving equations involving logarithms. They discuss the steps for solving the equations and using the inverse function of logarithms, exp(x), to find the value of x. The student makes a mistake in their calculations but is able to fix it with the help of the expert. The expert encourages the student to ask for help if they encounter any further difficulties.

#### Nx2

hi guys, I am not too sure how to do these questions:
solve for x,
a) (logx^3)^2 = logx^18
b) logx^3 + log(x^logx) = -2

so this is what i got so far:
a) (3logx)^2 = logx^18
9logx^2 = logx^18
18logx = logx^18
logx^18 = logx^18
... then i got stuck... i was clueless and did not know how to solve for x.

b) 3logx + (logx)(logx) = -2
logx^2 + 3logx +2 = 0
so let logx = s
s^2 +3s + 2 = 0
(s+1)(s+2)=0
s=-1 or s=-2
... then again i got stuck... I am not sure if what i did was right. our teacher gave us these questions that she has never taught us b4 and said this is ur assignment for the break... any help would be very much appreciated. thnx.

- Tu

a) You did an illegal operation btw line 2 and line 3 when you said 9logx^2 = 18logx

What you got here is $9(logx)^2$ and not $9log(x^2)$. And while it is true that $9log(x^2)=18logx$, it is not that $9(logx)^2=18logx$

b) You're almost there! you got the solutions s=-1 and s=-2, which translate into logx =-1 and logx=-2. Now you got to solve for x. Hint: Use the fact that $e^x$ is the inverse function of $logx$. This means that

$$e^{logx}=x$$

mmh.

oo... ok... so now that i have that... how do i solve for x in a though?

Nx2 said:
oo... ok... so now that i have that... how do i solve for x though?
see my last post. same trick.

srry.. but i don't think we learned e^x

Mmmh, did you learn about exp(x) ?

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yea i know exp(x)

They are the same.

$$\mbox{exp}(x) = e^x$$

So you know that exp(x) is the inverse function of logx, right?

Then exp(logx)=x.

ok.. but i still don't get how i would solve for x if i had
logx^18 = logx^18... wouldn't i just end up with 0 = 0?

err. you don't have logx^18 = logx^18. I told you there was a mistake between line 2 and 3. All you have is

$$9(logx)^2 = (logx)^{18}$$

If you don't see where to go from there, use the same substitution as you did in b). Set s = logx... then solve for s. Then use the fact that exp(s)=x to solve for x.

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omg... that's why it wasnt working... i was like so clueless... forgot bout that... thnx a lot man. i c what u meant when u were talking bout e^x now... thnx, very much appreciated for putting up with me.

It's all good. Don't hesistate to post if something doesn't work out!

## 1. What are logarithms and why do I need help with them?

Logarithms are mathematical functions that represent the inverse relationship of exponential functions. They are used to solve equations involving exponents and to convert between different forms of exponential expressions. Many students struggle with logarithms because they require a strong understanding of algebraic concepts.

## 2. How can I simplify logarithms?

To simplify logarithms, you can use properties such as the product, quotient, and power rules. These rules allow you to rewrite complicated logarithmic expressions into simpler forms. It is also helpful to understand the relationship between logarithms and exponents to simplify expressions.

## 3. How do I solve logarithmic equations?

To solve logarithmic equations, you can use the properties of logarithms to rewrite the equation in a simpler form. Then, you can solve for the variable using algebraic techniques. It is important to check for extraneous solutions when solving logarithmic equations.

## 4. What is the common base for logarithms?

The common base for logarithms is 10, also known as the base 10 logarithm or the common logarithm. This is because our number system is based on 10, making it the most convenient base for calculations. However, logarithms can also be written with other bases such as e, 2, or any positive number.

## 5. Can I use a calculator to solve logarithms?

Yes, most calculators have a logarithm function that allows you to solve logarithmic equations. However, it is important to understand the concepts and properties of logarithms in order to use a calculator effectively and to check for correct solutions.