I can't remember how to solve equations with logarithms/exponents

[Jamin2112]

This is frustrating me so much. I've been out of college for 1 year and I already forgot how to solve logarithm problems (though, to my surprise, I've encountered one I need to solve in real life.)

t₂/t₁ = (d₂/d₁)^1.06

and I need to solve for d₂.

I know the equation is the equivalent of

log_d2/d1(t₂/t₁) = 1.06,

but I still can't figure out how to isolate the d₂.

 

[Mark44]

This is frustrating me so much. I've been out of college for 1 year and I already forgot how to solve logarithm problems (though, to my surprise, I've encountered one I need to solve in real life.)

t₂/t₁ = (d₂/d₁)^1.06

and I need to solve for d₂.

I know the equation is the equivalent of

log_d2/d1(t₂/t₁) = 1.06,

but I still can't figure out how to isolate the d₂.

Start by taking the log of both sides.

 

[Jamin2112]

Start by taking the log of both sides.

log_1.06 of both sides?

 

[Mark44]

log₁₀ or ln, either one.

 

[Chestermiller]

Raise both sides to the 1/1.06 power.

Chet

 

[Jamin2112]

Raise both sides to the 1/1.06 power.

Wow, I feel like an idiot now. Was Mark44 trying to lead me down a rabbit hole?

 

[Chestermiller]

Wow, I feel like an idiot now. Was Mark44 trying to lead me down a rabbit hole?

No. Mark is a serious guy. He had a different approach in mind, probably motivated by your questions about logarithms.

Chet

 

[Jamin2112]

No. Mark is a serious guy. He had a different approach in mind, probably motivated by your questions about logarithms.

When I originally tried doing the "log to both sides, ..." approach, I started going in circles.

 

[paisiello2]

You need to use some basic identities of logarithms:
http://www.purplemath.com/modules/logrules.htm

 

[qspeechc]

Starting with logs seems like the hard way to me. Do what you usually do when you want to change the subject of a formula: get d2 on its own on one side.

First use the exponent rule: (a/b)^n = a^n/b^n, then re-arrange to get

d_2^1.06 = ...

Then continue.

EDIT: 'log rule' changed to 'exponent rule'

 

[Mark44]

Starting with logs seems like the hard way to me. Do what you usually do when you want to change the subject of a formula: get d2 on its own on one side.

First use the log rule: (a/b)^n = a^n/b^n, then re-arrange to get

That would be an exponent rule.

d_2^1.06 = ...

Then continue.

I agree that this approach is simpler, but taking logs of both sides isn't that much longer. After you take the natural log of both sides of the original equation, you have
$$ln(\frac{t_2}{t_1}) = 1.06 ln(\frac{d_2}{d_1})$$
Now divide both sides by 1.06 and exponentiate to get d₂/d₁ by itself. One more step and you're done.

The approach I suggested was just the first one to come to mind.

 

[qspeechc]

Slip of the tongue, so to speak ...:p