Logarithms where you are solving for X

[chemistudent]

Homework Statement

Put in Exponential form and solve for X. SHOW YOUR STEPS!

log₂(x-5)=5

Homework Equations

I am not sure what this is asking for. There are no other equations.

The Attempt at a Solution

2⁵=X-5

2⁵+5=X-5+5

32+5=X

X=37

 

[Dick]

Looks good to me. What's the question?

 

[chemistudent]

Looks good to me. What's the question?

How can I check this with a calculator? Because mine only has log₁₀

And if there isn't a way to check this with a calculator, Is there some website or something that i can use? Because when I look I can't find one.

 

[Dick]

You should be able to take log2(32) in your head. Since 32=2^5. But for future reference, log2(x)=log10(x)/log10(2).

 

[chemistudent]

You should be able to take log2(32) in your head. Since 32=2^5. But for future reference, log2(x)=log10(x)/log10(2).

um. I entered it into my calculator and I got an answer of 166.7025077 instead of 5.

I entered (log(37)/log(2))(X-5)

 

[Dick]

Put x=37. log2(x-5)=log2(37-5)=log2(32)=log10(32)/log10(2)=1.50515/0.30103=5. But again, this isn't a question where you need to rely on a calculator.

 

[chemistudent]

Put x=37. log2(x-5)=log2(37-5)=log2(32)=log10(32)/log10(2)=1.50515/0.30103=5. But again, this isn't a question where you need to rely on a calculator.

ok then.

um... one more question

3^(X+6)=27

log₃27=X+6

Aren't these the same thing?

And if they are is this how you would answer this question?

Homework Statement

Put in Exponential form and solve for X. SHOW YOUR STEPS!

3^(X+6)=27

log₃27=X+6

Homework Equations

I am not sure what this is asking for. There are no other equations.

The Attempt at a Solution

(log(27)/log(3))-6=X+6-6

3-6=X

X=-3

 

[Mark44]

Yes, the two equations are equivalent, which means essentially that they are both saying the same thing. Both have the same value of x as their solution.

In the first equation, 3^{x + 6} = 27, x + 6 represents the exponent on 3 that gives you 27. That means that x + 6 = 3, or equivalently, that x = -3.


In the second equation, log₃ 27 = x + 6, the left side simplifies to 3, giving you 3 = x + 6, or equivalently, x = -3.

Every time you have an exponential equation, there is an equivalent log equation that has the same solution (as long as the base is positive and not equal to 1). The opposite is also true; namely that every log equation has an exponential equation counterpart.