Solve for x: log10 x+ log10(x + 21) = 2.

Question

anonymous · Answer

$$\log_{10} x+\log_{10} (x+2)=2$$

anonymous · Answer

Use a scientific calculator, it may be helpful for your questions with logarithms.

anonymous · Answer

how do you plug it in a scientific calc

anonymous · Answer

Press the log button first then the value

anonymous · Answer

if it asks you to put a number before the log, put in a one, so it would be 1log10 and 1log10

anonymous · Answer

it's not working. I tried it with an easy log question like $$\log_{2} 8$$ and it gave me 1.806. This is what I put in I put the number 2 first then I pressed log then the number 8 but it gives me a decimal number

anonymous · Answer

that sounds about right

anonymous · Answer

I suggest getting help on scientific plug-ins, either with a teacher, a family member that may know, or a student/friend.

anonymous · Answer

I think I figured it out.

$$\log_{10} x+\log_{10} (x+21)=2$$
$$\log_{10} x(x+21)=2$$
$$10^{2}=x ^{2}+21x$$
$$100=x ^{2}+21x$$ $$-100    -100$$
$$0=x ^{2}+21x-100$$
$$0=(x+25)(x-4)$$
$$x=-25,4$$

What do you think?

anonymous · Answer

In order for it to work in your calculator you just divide log with the base into log with the result. Example: $$\log_{2} 8$$ in order to find that you simply divide log 2 into log 8. So log 8 divide by log 2 and it will give you the answer. But don't divide it in fraction form because it will give you a decimal number.

anonymous · Answer

In school when I used that, we always got a decimal and rounded it to the nearest hundredth.

anonymous · Answer

If you divide it in fraction form you get a decimal but if you just simply divide it using the division button it simply gives you the whole number.

loser66 · Answer

reject -25, so the solution is x =4

anonymous · Answer

They both work bro

mathstudent55 · Answer

@Tehsh
You solved it correctly. Now you need to look at both answers, x = -25, x = 4, and plug them into the original equation. The log is not defined for negative numbers or zero, so log10 (-25) and log10 (-25 + 21) have no meaning, so the solution x = -25 must be discarded. the ony solution is x = 4

mathstudent55 · Answer

@Loser66 is correct.

anonymous · Answer

Oh ya I made a huge mistake. He was right. In order to solve for log they must be greater than 0 because there is nothing you can square a number to to get 0 or -1. I accidentally plugged it into 0=x ^{2}+21x-100. I made a rookie mistake!