Change of Base Formula for Logs
Read this topicExplanations 3
- The Change of Base Formula Let's say you have a somewhat mediocre calculator; one that can only calculate logs in base 101010. Now let's think about how we would approximate som…
By Ivan Hu, Alex Federspiel, Eunji Kwon, Anusha Rahman
- (Video) Change of Base Formula by mathman1024 Here's a video by mathman1024 going over the Change of Base Theorem. The common logarithm is in base 101010. When writing the commo…
By Alex Federspiel, Eunji Kwon, Anusha Rahman
- Now that we've learned how to add and subtract logs, we can move onto more complicated math with logs. Change of Base Formula for Logs We know that logarithms can have many diff…
By Trisha, Anusha Rahman
Problems 22
- Compute log23⋅log34⋅log45⋅log56⋅log67⋅log78\log_2 3 \cdot \log_3 4 \cdot \log_4 5 \cdot \log_5 6 \cdot \log_6 7 \cdot \log_7 8log23⋅log34⋅log45⋅log56⋅log67⋅log78.
- Evaluate log23⋅log34\log_2 3 \cdot \log_3 4log23⋅log34.
- Compute log6416⋅log279\log_{64} 16 \cdot \log_{27}9log6416⋅log279.
- Suppose that a circle has radius ln(R3)\ln (R^3)ln(R3) and circumference ln(C6)\ln (C^6)ln(C6). Find logRC\log_R ClogRC.
- Evaluate log12536log56.\frac{\log_{125} 36}{\log_5 6}.log56log12536.
- Evaluate log47⋅log74\log_4 7 \cdot \log_7 4log47⋅log74.
- For every x≥−1ex \ge -\frac{1}{e}x≥−e1, there is a unique number W(x)≥−1W(x) \ge -1W(x)≥−1 such that W(x)eW(x)=x.W(x) e^{W(x)} = x.W(x)eW(x)=x. The function WWW is called Lambe…
- Let bbb, xxx, and nnn be constants greater than 1. Simplify logbn(xn)\log_{b^n}(x^n)logbn(xn).
- Evaluate the following: loge2e−lne2\log_{e^2}e - \ln e^2loge2e−lne2
- Solve for xxx: logx10+logx210=6\log_{x}10 +\log_{x^{2}}10 = 6logx10+logx210=6
- Solve for xxx: log2x+log4x+log16x=7\log_{2}x+\log_{4}x+\log_{16}x = 7log2x+log4x+log16x=7
- Solve the expression using the change of base formula. log236\log_{2}36log236
- Solve for xxx: log3x+log27x=9\log_{3}x+\log_{27}x = 9log3x+log27x=9
- Evaluate logx16⋅log4x\log_{x}16 \cdot \log_{4}xlogx16⋅log4x
- Solve for yyy: logy39+logy9=15\log_{y^3}9+\log_{y}9= 15logy39+logy9=15
- Evaluate logx225⋅log5x2\log_{x^{2}}25 \cdot \log_{5}x^{2}logx225⋅log5x2
- Solve for xxx: logx416+logx16=20\log_{x^{4}}16+\log_{x}16 = 20logx416+logx16=20
- Solve for xxx: log4(x+2)−log16(x2−4)=1\log_{4}(x+2)-\log_{16}(x^{2}-4) = 1log4(x+2)−log16(x2−4)=1
- Solve for xxx: log5x+log7x=log25x\log_{5}x+\log_{7}x= \log_{25}xlog5x+log7x=log25x
- Solve for xxx: log8x−log16x=0\log_{8}x -\log_{16}x = 0log8x−log16x=0
- Solve for xxx in the equation logx55+logx25=11\log_{x^{5}}5 + \log_{x}25=11logx55+logx25=11.
- Evaluate log133⋅log313\log_{13}3 \cdot \log_{3}13log133⋅log313.