All Questions
Tagged with algebra-precalculus logarithms
1,540
questions
3
votes
2
answers
275
views
A problem that could use substitution or logs, not sure which works better
This is one of those brain teaser problems on instagram, and it starts here:
$$x^{x^2-2x+1} = 2x + 1$$
And we want to solve for x. My first instinct was to try this
$$\ln(x^{x^2-2x+1}) = \ln(2x + 1)\\
...
- 2,692
-2
votes
0
answers
139
views
Solving $\sqrt{x+1}=-2$ and looking for complex solutions [duplicate]
So the question was
$$\sqrt{x+1}=-2$$
And obviously there is no value for it,
However,
If you do the thing with $e$ and $\ln{}$
$$e^{\ln{\sqrt{x+1}}}$$
and
$$e^{\frac{1}{2}\cdot (\ln{x+1})}$$
Then ...
- 19
0
votes
1
answer
40
views
How to solve for a value in a log
I have a formula:
Weight=onerepmax*(0.488 + 0.538 * ln(-0.075*reps))
And I need to solve for reps given a onerepmax and a weight.
I got as far as:
...
- 113
-5
votes
2
answers
72
views
If the domain of $f(x)$ is $(-3, 1)$, then what is the domain of $f(\ln x)$? [closed]
I need a clear explanation for this question:
If the domain of $f(x)$ is $(-3, 1)$ then the domain of $f(\ln x)$ is ...
a) $\;(e^{-1}, e^3)$
b) $\;(0, \infty)$
c) $\;(1, \infty)$
d) $\;(e^{-3}, e^...
0
votes
6
answers
194
views
How would you prove $\log_{2}x < \sqrt x$ for $x > 16$? [closed]
I'm not really showing how to prove this, since I tried finding the $x$-intercepts/zeros of $f(x) = \sqrt x - \log_{2} x$ , and see that $x = 4, 16$ work but inspection, but I'm not sure how to ensure ...
- 865
-3
votes
2
answers
191
views
How do you solve this equation $ \log_{2}(x) = \sqrt x$? [closed]
Disclaimer: Guys before voting to get the question closed I strongly feel we should instead have a feature on MSE that can merge such similar/duplicate questions since we got some really cool/through ...
- 865
2
votes
1
answer
88
views
Solving $\frac{\ln(y/x)}{y-x} = t$ for $x$ [duplicate]
I am having trouble solving an algebra formula which is for a project of mine.
I must solve for $x$ ($y$ is a known value).
$$\frac{\ln\left(\dfrac{y}{x}\right)}{y-x} = t$$
As I try to solve the ...
- 29
1
vote
1
answer
41
views
What to consider when taking kth root on both sides of equality
Say I have the following expression:
$10^{l} = a^{k}$
If I take the kth root of both sides, does that mean we get:
$10^{\frac{l}{k}} = a$
We don't have to consider anything with plus or minus?
- 865
1
vote
2
answers
71
views
Log X to what base n yields a whole number [closed]
Does there always exist a real number 'n' such that $log_{n}x$ is a whole number for any real number x?
If yes what would the function to find this number look like?
- 11
0
votes
0
answers
33
views
Why is there no logarithmic form of the exponential distributive rule/power of a product rule?
When learning the laws of exponents and logarithms, one finds that there is a correspondence. Each law of exponents has a corresponding equivalent expression in terms of logarithms. For example, the ...
- 16.9k
1
vote
4
answers
921
views
Why roots aren't the inverse of exponentiation but logarithms?
I think it's easy to see it when we look at the inverse of the function "$f(x) = a^x$" but I wonder if there's other way to look at it besides just analyzing the function. I was taught my ...
- 21
1
vote
5
answers
100
views
If $\log_7 5$ = a , $\log_5 3$ = b , $\log_3 2$ = c, then the logarithm of the number 70 to the base 225 is?
So, I've tried using the properties:
$$\log_a b = \frac{\log_c b}{\log_c a}$$
and..
$$\log_a bc = \log_a b + \log_a c$$
And, the final simplification should be in the following options:
$$A. \frac{1-a+...
- 13
3
votes
2
answers
151
views
Logarithmic inequality involving $a_1, a_2, ..., a_n$
Given the real numbers $a_1, a_2,...,a_n$ all greater than $1$, such that $\prod_{i=1}^{n} a_i=10^n$, prove that:
$$\frac{\log_{10}a_1}{(1+\log_{10}a_1)^2}+\frac{\log_{10}a_2}{(1+\log_{10}a_1 + \log_{...
- 409
4
votes
1
answer
131
views
Reducing product of powers of logarithm
I am trying to show that
$$(\log(a))^n (\log(b))^m = P(\log(a^ib^j)), \quad i,j \in \{-1,0,1\}$$
where $P$ is a polynomial and $n \ge m \ge 1$ are natural numbers. Using Binomial identities for the ...
- 3,290
1
vote
3
answers
113
views
How to solve $x+1=5e^{4x}$ [closed]
How to solve $x+1=5e^{4x}$
In general, I know to take ln() of both sides to bring down the exponent for e, but the left side is also a variable.
- 4,771