All Questions
10
questions
1
vote
1
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71
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Solving Logarithmic Expression
In the context of the thermodynamics of mixing two separate gases at the same temperature and pressure, one has the generic equation,
\begin{gather*}
-\frac{\Delta S_{mix}}{nR} = X_A \ln(X_A) + X_B \...
- 165
1
vote
4
answers
124
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Describe the set of real numbers $x$ which satisfy $2\log_{2x+3}x<1$.
Describe the set of real numbers $x$ which satisfy $2\log_{2x+3}x<1$.
Here, I am really stuck . In this problem, I tried to compute by writing this expression as $(2x+3)^a=x^2$, where $a<1$. ...
- 2,624
3
votes
3
answers
86
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Find $\log_e3 - \frac{\log_e9}{2^2} + \frac{\log_e27}{3^2} - \frac{\log_e81}{4^2} + ...$
Find $\log_e3 - \dfrac{\log_e9}{2^2} + \dfrac{\log_e27}{3^2} - \dfrac{\log_e81}{4^2} + ...$
What I Tried:- This is the same as :-
$$\ln3 - \frac{\ln3}{2} + \frac{\ln3}{3} - \frac{\ln3}{4} + \dots$$
$$...
- 4,254
1
vote
5
answers
139
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Simplify $2\log 4 + 3\log 8 - \log 2$ using logarithmic laws, then evaluate.
Firs time I've encountered this type of question where there is a number in front of the log, and it's throwing me a bit. I'm fine with using the logarithmic laws to simplify, but not sure if I need ...
- 57
3
votes
2
answers
97
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Exponent equation with common power
Solve for $x$ in
$$\log_{2}(2^{x-1}+3^{x+1}) = 2x-\log_{2}(3^x)$$
I simplified by doing:
$$\log_{2}(3^x \cdot 2^{x-1} + 3^{2x+1}) = 2x$$
$$\frac{6^x}{2} + 3^{2x+1} = 2^{2x}$$
$$6^x + 2 \cdot 3^{2x+1} =...
- 419
0
votes
2
answers
147
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How to solve: $20\cdot x\cdot\log_2 x=1000000$
$$20\cdot x\cdot\log_2 x=1000000$$
I tried but it is pretty strange to me. Thanks for your help!
-2
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1
answer
392
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How to solve $\log_2(x) +3 = \log_3(x+2)$ [closed]
Hi Math Stack Exchange Communities,
I am new here. I have a question regarding logarithm solving.
Let's say I have this equation:
$$\log_2 (x) +3 = \log_3 (x+2)$$
How can I solve this kind of ...
- 175
2
votes
6
answers
274
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Why isn't $-2$ solution for $x$?
I came across an logarithm problem recently. I don't know why solution to this problem cannot be $-2$. Now, don't downvote now because you don't know why I'm asking this. I know that logarithms' ...
- 3,875
3
votes
2
answers
154
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Is it possible to solve this equation with logarithms and exponents?
$$-\frac{1}{3}\log(4x-12)+6=\left(-\frac{1}{2}\right)^x $$
Out of all the logarithm laws I've learned (which is pretty limited), I have not found a way to solve for what x is yet. Can someone verify ...
- 518
3
votes
1
answer
104
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How to compute a product of logarithms?
I've been reading through Stewart's Calculus textbook, and came across the following problem fairly early on -
What is $$\prod_{i = 2}^{31} \log_i (i + 1)\;?$$
I did some searching, and found that ...
- 4,695