Intro to Adding and Subtracting Logs (Same Base)
Read this topicExplanations 6
- (Video) Properties of Logarithms by PatrickJMT This video by PatrickJMT covers addition and subtraction with logs of the same base. Summary\large{\text{Summary}}Summary The rule…
By Alex Federspiel, Amy Feraco, Jonathan Heller
- (Video) Combining Logarithmic Expressions by ThinkwellVids This video by ThinkwellVids video goes over some more complex logarithm examples. Summary\large{\text{Summary}}Summary…
By Alex Federspiel, Amy Feraco, Jonathan Heller
- (Video) Properties of Logarithms by yaymath This video by yaymath explains the properties of logarithms and works through some practice problems. Summary\large{\text{Summary}}Su…
By Alex Federspiel, Liza Sulkin, Amy Feraco, Jonathan Heller, Anusha Rahman
- Laws of Logs Here's a summary of all the useful algebraic properties of logs that you can use! Basic facts and identities: loga1=0\log_{a}1=0loga1=0 logaa=1\log_{a}a=1logaa=…
By Liza Sulkin, Anusha Rahman
- Logarithm addition and subtraction logab+logac=logabc\log_ab+\log_ac=\log_abclogab+logac=logabc logab−logac=logabc\log_ab-\log_ac=\log_a\frac{b}{c}logab−logac=logacb…
By Liza Sulkin, Alex Federspiel, Evan Fang, Amy Feraco, Anusha Rahman
- Adding and Subtracting Logs (Same Base)
By Trisha, Anusha Rahman
Problems 31
- Simplify loga3+loga5\log_a 3+\log_a 5loga3+loga5 if a>1a>1a>1.
- Simplify loga7+loga4\log_a 7+\log_a 4loga7+loga4 if a>1a>1a>1.
- Simplify loga4+loga16\log_a 4+\log_a 16loga4+loga16 if a>1a>1a>1.
- Which of the following equal loga(6xy),\log_a (6xy),loga(6xy), if a>1a>1a>1 and x,y>0x,y>0x,y>0?
- loga20\log_a 20loga20 can also be written as...
- Simplify loga15+loga6\log_a 15+\log_a 6loga15+loga6 if a>1a>1a>1.
- Simplify loga2+loga3\log_a 2+\log_a 3loga2+loga3 if a>1a>1a>1.
- Solve for xxx. lnx+ln(x+2)=4\ln x+\ln(x+2)=4lnx+ln(x+2)=4
- What is the sum of the positive real solutions to (log2x)2=log2(x4)(\log_2 x)^2 = \log_2(x^4)(log2x)2=log2(x4)?
- How many distinct positive real roots does the equation log10(x6)=(log10x)3\log_{10}(x^6) = (\log_{10}x)^3log10(x6)=(log10x)3 have?
- How many distinct positive real roots does the equation (log10(x6))2=(log10x)3(\log_{10}(x^6))^2 = (\log_{10}x)^3(log10(x6))2=(log10x)3 have?
- Compute log242+log243+log244\log_{24} 2 + \log_{24} 3 + \log_{24} 4log242+log243+log244.
- If k>0k>0k>0, simplify the following expression: log381k+log327k\log_3 81k + \log_3 \frac {27}klog381k+log3k27.
- Simplify log234+log245+log256\log_2 \frac34 + \log_2 \frac45 + \log_2 \frac56log243+log254+log265.
- Simplify log(2x)+log(x)\log\left(2x\right)+\log\left(x\right)log(2x)+log(x) for x>0x>0x>0
- Simplify log(2)+log(12)+log(x)\log\left(2\right)+\log\left(\frac{1}{2}\right)+\log\left(x\right)log(2)+log(21)+log(x) for x>0x>0x>0
- Simplify log(2x)+log(4y)+log(3z)\log\left(2x\right)+\log\left(4y\right)+\log\left(3z\right)log(2x)+log(4y)+log(3z) for x,y,z>0x,y,z>0x,y,z>0
- Simplify log(4a)+log(2b)\log\left(4a\right)+\log\left(2b\right)log(4a)+log(2b) for a,b>0a,b>0a,b>0
- Simplify ln(16e)+ln(6e)\ln\left(\frac{1}{6}e\right)+\ln\left(6e\right)ln(61e)+ln(6e)
- Simplify log(2x)−log(x)\log\left(2x\right)-\log\left(x\right)log(2x)−log(x) for x>0x>0x>0
- Simplify log(10a2)−log(2a)\log\left(10a^2\right)-\log\left(2a\right)log(10a2)−log(2a) for a>0a>0a>0
- Simplify log(2)−log(12)\log\left(2\right)-\log\left(\frac{1}{2}\right)log(2)−log(21)
- Simplify log(x3+x2)−log(x2)\log\left(x^3+x^2\right)-\log\left(x^2\right)log(x3+x2)−log(x2)
- Simplify log(13)−log(16)\log\left(\frac{1}{3}\right)-\log\left(\frac{1}{6}\right)log(31)−log(61)
- Solve for xxx: ln2x−ln(x−6)=ln8\ln 2x - \ln(x-6) = \ln 8ln2x−ln(x−6)=ln8
- Simplify loga(12)+loga(12)\log_{a}(12) + \log_{a}(12)loga(12)+loga(12) when a>1a>1a>1.
- Simplify the expression log7(4)+log7(12)−log7(8).\log_7(4) + \log_7(12) - \log_7(8).log7(4)+log7(12)−log7(8).
- Which of the following ordered pairs (a,b)(a, b)(a,b) satisfy the equation log5(64)=log5(a)+log5(b)?\log_{5}(64) = \log_5(a) + \log_5(b)?log5(64)=log5(a)+log5(b)?
- The Pittsburgh Pirates play the St. Louis Cardinals on April 1, 2019 (see here for more info). Let's say the probability of the Pirates winning this game is PPP. Then we define …
- Simplify log4(12)−log4(4)+log4(163).\log_4(12) - \log_4(4) + \log_4\left(\frac{16}{3}\right).log4(12)−log4(4)+log4(316).
- Let λ∈(0,1).\lambda \in (0, 1).λ∈(0,1). Find the value of limx→∞ln(xλ(x+1)λ−1)λx+(1−λ)(x+1).\lim_{x \rightarrow \infty}\frac{\ln\left(\frac{x^{\lambda}}{(x + 1)^{\lambda - 1}}…