Evaluating Logs Using Rules
Read this topicExplanations 3
- Good news, logarithms that are not in base 101010 have the exact same rules as logs with base 101010! The only difference is the base. As we learned before, if the base of a log…
By Rithwik Mylavarapu, Eunji Kwon, Anusha Rahman
- (Video) Use laws of logarithms to simplify a logarithmic function (KristaKingMath) by Krista King Watch this video by Krista King to learn how to evaluate logs using log rules! …
By Trisha, Anusha Rahman
- Evaluating Logs Using Rules In the next couple of lessons, you'll learn to solve log equations with the same base and solve log equations with properties. You'll end this sectio…
By Trisha, Anusha Rahman
Problems 20
- Given that a=log2a = \log 2a=log2 and b=log3b = \log 3b=log3, express log12\log 12log12 in terms of aaa and bbb.
- What is log2164\log_2 \frac1{64}log2641?
- Evaluate log3729\log_3 729log3729.
- Compute log8(16)\log_8(16)log8(16).
- How many positive integer values of bbb have the property that logb64\log_b 64logb64 is a positive integer?
- If x=(log322)log232x = (\log_{32} 2)^{\log_2 32}x=(log322)log232, compute log5x\log_5 xlog5x.
- What is log42\log_4 2log42?
- Evaluate: log3(7log7(108))−log3(log2(16))\log_3(7^{\log_7(108)}) - \log_3(\log_2(16))log3(7log7(108))−log3(log2(16))
- Evaluate log5625\log_5 625log5625.
- Evaluate log9(log28)\log_9\left(\log_28\right)log9(log28)
- Evaluate log2(log5625)\log_{2}(\log_{5}625)log2(log5625).
- If x=log28x=\log_2{8}x=log28, evaluate logx81\log_{x}81logx81.
- Evaluate log646656\log_{6}46656log646656.
- Evaluate log4(log3(27)+log3(3))\log_{4}(\log_{3}(27) +\log_{3}(3))log4(log3(27)+log3(3)).
- Evaluate log7343\log_{7}343log7343.
- Evaluate log2(log465536)\log_{2}(\log_{4}65536)log2(log465536).
- Evaluate log6(log2128−log22)\log_{6}(\log_{2}128 - \log_{2}2)log6(log2128−log22).
- Evaluate log4(256)\log_4(256)log4(256).
- log5(875)\log_5(875)log5(875) can be written in the form A+Blog5(C)A + B\log_5(C)A+Blog5(C) for positive integers A,B,A, B,A,B, and CCC. What is A+B+CA + B + CA+B+C?
- Evaluate the sum ∑n=12019ln(n+1n).\sum^{2019}_{n = 1}\ln\left(\frac{n + 1}{n}\right).n=1∑2019ln(nn+1).