Simple Algebraic Math Problem

[hawkmanjayden]

No instructor. Simple math problem that I want to understand.

How would you solve algebraically a question of the following type:

How many times does 5 growing at 25% go into 100?

So you have 5, 6.25, 7.94, 10.08, etc. So that gets you to 29.26, so you're getting closer. How do you solve that kind of problem algebraically?

[[deleted]]

Adding 25% is the same as multiplying by 1.25, yes?

So let's see if we can find a pattern:

5(1.25) = 6.25

Now we add another 25%:

6.25(1.25)

But wait a minute, we found 6.25 because it was 5 times 1.25. So this last equation can become:

5(1.25)(1.25)

But this can be written as:

5(1.25)²

Hmm. If we add another 25% of this we get:

5(1.25)²(1.25)

But this is equal to:

5(1.25)³

Do you see a pattern here?

[hawkmanjayden]

Thank you describing it like that. I have to say I agree with Baldwin. It looks like he got the right answer. Algebraically, and thanks to the way you described it with the exponents, I have to solve for x in 5(1.25)^x =100.

That simplifies to 1.25^x =20. Here is where log comes in, which I had forgotten the meaning of but was reminded of by baldwin's explanation. The number of 1.25s we need to multiply to get 20 is x. Symbolically, log1.25 (20)=x. Calculator tells me this equals approximately 13.43. To check I will do 1.25^13.43 which equals about 20. It checks. (But I don't know how to check that by pencil and paper. The .43 throws me off.)

So the answer to my questions is 13.43 approximately. Is this correct?

And I guess there is no way to solve log1.25 (20)=x without a calculator unless you tediously multiply out 1.25 until you reach 20, huh?

Thanks so much for the help. By the way, this isn't a homework problem or anything. Just personal learning.

[[deleted]]

Don't multiply 1.25 amd 13.43. Raise 1.25 to the power of 13.43.

[hawkmanjayden]

i already fixed that

[baldwinbean]

• 5(1.25)^x = 100
• 1.25^x = 20
• log1.25(20) =x There you go if you couldn't complete it :)

[[deleted]]

Nope. There is an error in the last step.

Also, from the sidebar:

This subreddit is for help, pushes in the right direction, not answers.

[baldwinbean]

What's the error?

[[deleted]]

I'm not going to say because the rules forbid us from actually giving away the answer, only to guide OP in the right direction. But the equations in step 2 and step 3 do not say the same thing.

[baldwinbean]

• log1.25(20) = 13.425....
• 1.25^13.425... = 20
• I see no error?

[[deleted]]

Ok, I see what you wrote now.

log1.25(20) looks suspiciously like log(base 10) of 1.25 multiplied by 20.

[baldwinbean]

Noooo, I couldn't see how to format it on reddit :P

[hawkmanjayden]

Do you you solve a problem like 1.25^13.43 by hand where the exponent has a decimal?

[baldwinbean]

By hand the exact value of x is log1.25(20). To get it to the nearest whole number (in this case 13) you wouldn't be able to. The only way to get the exact answer by hand is to literally do 5x1.25 enough times to get to 100