All Questions
Tagged with algebra-precalculus logarithms
1,541
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How do I solve for $V$ in this equation?
$$\frac{\ln(T+1)-\ln(V-S+1)}{\ln(V-S+1)}=\frac{1}{K}-1$$
What are the steps if I want to solve for $V$?
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Calculate reproduction rate
If I knew that by the year 2000 that there were 1 trillion humans, and that they started reproducing 2000 years before that, how would I calculate their birth rate?
Assume an initial population of 1 ...
- 131
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Simplifying this expression
How to simplify this?
$\displaystyle\frac{n^{\log m}}{m^{\log n}}$
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If $ x = \log_{12} 27 \text {,then what is the the value of } \log_6 16 $?
How to proceed in this problem ?
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Any tricky method to solve this one?
The question :
Prove that :$$ \text{ if } y = 2x^2 - 1,\text{ then } \biggl[ \frac{1}{y} + \frac{1}{3y^3} + \frac{1}{5y^5}+ \cdots \biggr]$$ is equal to $$\frac{1}{2} \biggl[ \frac{1}{x^2} + \frac{1}{...
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How to derive the following series expansion for $\ln \left( \frac{x+1}{x-1} \right)$?
How to prove :
$$ \ln \biggl(\frac{x+1}{x-1}\biggr) = 2\biggl[\frac{1}{x} + \frac{1}{3x^3} + \frac{1}{5x^5} + \cdots \biggr]$$ where $|x| \gt 1$
I am not able to get how to proceed on this one ?
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Domain Problem: $\sqrt{ \log_{\frac{1}{2}} x}$
How to find the domain of the function $\sqrt{ \log_{\frac{1}{2}} x}$ ?
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How $a^{\log_b x} = x^{\log_b a}$?
This actually triggered me in my mind from here. After some playing around I notice that the relation $a^{\log_b x} = x^{\log_b a}$ is true for any valid value of $a,b$ and $x$. I am very inquisitive ...
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Proving Logarithmic identity
Today, I read these two new Logarithmic identity $\displaystyle$ $$a^{\log_a m} = m $$ $$\log_{a^q}{m^p} = \frac{p}{q} \log_a m$$ Both of them seems new to me,so even after solving some problems (...
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Solving $\log _2(x-4) + \log _2(x+2) = 4$
Here is how I have worked it out so far:
$\log _2(x-4)+\log(x+2)=4$
$\log _2((x-4)(x+2)) = 4$
$(x-4)(x+2)=2^4$
$(x-4)(x+2)=16$
How do I proceed from here?
$x^2+2x-8 = 16$
$x^2+2x = 24$
$...
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Is it true that $x^{\log_z(y)} = y^{\log_z(x)}$?
it has been years since I have done logs, I remember something like this:
$$x^{\log_z(y)} = y^{\log_z(x)}$$
(where $z$ is the base)
Is that correct? It doesn't seem so, since
$$3^{\log_2(4)} \neq ...
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