Need someone to check my work

[abel muroi]

I was given the problem 60 = 24 * 1.05^x + 10 and was told to solve for x.

Here is my work..

60 = 24 (x) log1.05 + 10
60 = 24 (x) + 10.0211893
49.9788 = 24x
2.0825 = x

did i do this correctly?

 

[Ishuda]

I was given the problem 60 = 24 * 1.05^x + 10 and was told to solve for x.

Here is my work..

60 = 24 (x) log1.05 + 10
60 = 24 (x) + 10.0211893
49.9788 = 24x
2.0825 = x

did i do this correctly?

No, not quite. Start with
60 = 24 * 1.05^x + 10
and group all but the 1.05^x on one side
\(\displaystyle 1.05^x = \frac{60 - 10}{24} = \frac{50}{24}\) ~ 2.08333333333

Now take the log.

 

[abel muroi]

No, not quite. Start with
60 = 24 * 1.05^x + 10
and group all but the 1.05^x on one side
\(\displaystyle 1.05^x = \frac{60 - 10}{24} = \frac{50}{24}\) ~ 2.08333333333

Now take the log.

ok I re-did the problem and here is what i got.

60 = 24 * 1.05^x + 10
50 = 24 * 1.05^x ((divide both sides by 24))
2.083333333 = 1.05^x
log 2.083333333 = (x) log 1.05

15.043384 = x

did i do it correctly this time?

p.s why can't i add 24 to both sides?

 

[Ishuda]

ok I re-did the problem and here is what i got.

60 = 24 * 1.05^x + 10
50 = 24 * 1.05^x ((divide both sides by 24))
2.083333333 = 1.05^x
log 2.083333333 = (x) log 1.05

15.043384 = x

did i do it correctly this time?

p.s why can't i add 24 to both sides?

Yes, you did it correctly.

If you add 24 to each side, you just get back to where you were except, instead of a 10, you would have a 24, i.e.
74 = 24 * 1.05^x + 24

 

[abel muroi]

Yes, you did it correctly.

If you add 24 to each side, you just get back to where you were except, instead of a 10, you would have a 24, i.e.
74 = 24 * 1.05^x + 24

sorry i meant SUBTRACT 24 from both sides, not add. If i subtract 10 from both sides shouldn't i subtract 24 from both sides as well?

60 = 24 * 1.05^x + 10 ((can i subtract 24 and 10 from both sides?))
26 = 1.05^x

would this method also work?

 

[ksdhart]

You don't want to subtract 24 in this case because it's a multiplication problem, not an addition problem. After subtracting the 10, the problem you have is:

50 = 24 * 1.05^x

That's 24 times 1.05 to the x, so to get rid of the 24, you'd divide by 24, like you did the second time when you got the right answer.