Common log question (are you done?)

[Edin_Dzeko]

the rule states, log x => log 10^x

the problem said to evaluate / solve and show work. so:

log 1000 = log 10 ^ 1000. I'm I done at that point or do I have to go on and solve it?

log 10^1000 = x
10 ^ x = 1000
x = 3

which one goes? do I leave it as log 10 ^ 100 or because the problem says to evaluate I have to go on and solve and put the x = 3?

 

[Mark44]

the rule states, log x => log 10^x

There is no rule like this. Are you thinking of this one?

x = log(10^x)

the problem said to evaluate / solve and show work. so:

log 1000 = log 10 ^ 1000.

You're way off here. log(10¹⁰⁰⁰) = 1000, while log 1000 = 3.

I'm I done at that point or do I have to go on and solve it?

log 10^1000 = x
10 ^ x = 1000
x = 3

which one goes? do I leave it as log 10 ^ 100 or because the problem says to evaluate I have to go on and solve and put the x = 3?

 

[Edin_Dzeko]

there is no base written for the log and so the rule is:
If there is no base for the log it is understood to be base 10.

log x = log 10^x that's the rule.

and the problem is log 1000. so log 10 ^1000

 

[LCKurtz]

there is no base written for the log and so the rule is:
If there is no base for the log it is understood to be base 10.

log x = log 10^x that's the rule.

I think you must mean

$$\log(x) = log_{10} (x)$$

so

$$\log(1000) = log_{10} (1000) = log_{10}(10^3) = 3$$

 

[Mark44]

there is no base written for the log and so the rule is:
If there is no base for the log it is understood to be base 10.

log x = log 10^x that's the rule.

What you have written is different from what you mean.

If there is no base given for a log, it is often (not always) understood to mean base 10. In other contexts, log x can mean ln x (i.e., log_e x) or log₂ x.

What you should write is log x = log₁₀ x.

10^x means 10 raised to the power of x.

and the problem is log 1000. so log 10 ^1000

No. log 1000 = log₁₀ 1000. When you write 10^1000, that means 10 raised the the power 1000, which is 1 followed by 1000 zeros.

log 1000 = log 10³ = ?

 

[Edin_Dzeko]

What you have written is different from what you mean.

If there is no base given for a log, it is often (not always) understood to mean base 10. In other contexts, log x can mean ln x (i.e., log_e x) or log₂ x.

What you should write is log x = log₁₀ x.

10^x means 10 raised to the power of x.

No. log 1000 = log₁₀ 1000. When you write 10^1000, that means 10 raised the the power 1000, which is 1 followed by 1000 zeros.

log 1000 = log 10³ = ?

oh okay. sorry guys. the confusion comes from me. i don't know how to do the base correctly. I didn't mean to the 10th power I meant base and the number is in the top left hand. I'm sorry for that mistake. Really glad you understood what I meant. I don't know how to do the base properly. for future references how do you do it? can you show me?

Btw, the poster above you has clarified it so I understand now. Thanks guys.

 

[Mark44]

You can make subscripts by typing the tags by hand or by using the advanced menu.
To make them by hand, use [ sub] and [ /sub] tags around the subscript, but without the leading spaces.

For example, log[ sub]10[ /sub] 1000. I have the extra spaces so you can see what the tags look like. The same expression, without the extra spaces, renders as log₁₀. You can do exponents in a similar way using the [ sup] and [ /sup] tags (again, no extra spaces inside the brackets, and the exponent between the two tags.

For example, 10[ sup]3[ /sup] = 1000. Without the extra spaces, this renders as 10³ = 1000.

The other way is to use the advanced menu, which appears when you click Go Advanced. The X₂ button can be used to make subscripts, and the X² button can be used to make superscripts (exponents).