Simple algebraic / logarithmic question

[mofoj]

Homework Statement

(1.024)^2 = (1 + m)^12

Homework Equations

The Attempt at a Solution

1.048576 = (1+m)^12
I tried to do a square root of 12 for both sides but does not appear to be correct. I've also tried doing log to bring the exponents to the front for both sides, but something is wrong. I learned this long time ago so I really can't remember how to approach it.

 

[Borek]

I guess you are trying to solve for m?

Starting with a 12^th root of both sides seems like a reasonable way of dealing with the exponent.

 

[mofoj]

I guess you are trying to solve for m?

Starting with a 12^th root of both sides seems like a reasonable way of dealing with the exponent.

Yeah that's what I did, but I did not get the correct answer, which should be 0.003961.

 

[eumyang]

What did you get when you took the 12th root of 1.048576? And did you subtract 1 from both sides after taking the 12th root?

 

[mofoj]

What did you get when you took the 12th root of 1.048576? And did you subtract 1 from both sides after taking the 12th root?

yes I did subtract the 1 after, but it is not the correct answer still.

 

[Mark44]

Show us what you did...

 

[mofoj]

Show us what you did...

1.048576 = (1+m)^12

12th sq root
10.69516372 = 1 + m
9.69516372 = m


supposed to be 0.003961

 

[Mark44]

1.048576 = (1+m)^12

12th sq root
10.69516372 = 1 + m
9.69516372 = m


supposed to be 0.003961

There's no such thing as a "12th sq root". You raised the left side to the 12th power. That's different from taking the 12th root, which is the same as the 1/12 th power.

1.048576 = (1+m)^12
(1.048576)^(1/12) = 1+m

 

[mofoj]

There's no such thing as a "12th sq root". You raised the left side to the 12th power. That's different from taking the 12th root, which is the same as the 1/12 th power.

1.048576 = (1+m)^12
(1.048576)^(1/12) = 1+m

finally! great, thanks for the help.

 

[HallsofIvy]

There's no such thing as a "12th sq root".

A very good point. Unfortunately, even the "LaTex" used on this board requires that we enter a "12th root" as \sqrt[12]{x} !

You raised the left side to the 12th power. That's different from taking the 12th root, which is the same as the 1/12 th power.

1.048576 = (1+m)^12
(1.048576)^(1/12) = 1+m

 

[zgozvrm]

You can simplify things a bit by doing this:

$$1.024^2 = (1 + m)^{12}$$

$$\left( 1.024^2 \right) ^{1/12} = \left[ (1 + m)^{12} \right]^{1/12}$$

$$1.024^{1/6} = 1 + m$$

$$\sqrt[6]{1.024} = 1 + m$$

$$m = \sqrt[6]{1.024} - 1$$
At least it keeps the numbers nice and tidy until the end!