Solving Log Equations Using Properties
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- Solving Log Equations Using Properties We've covered how to solve log equations with the same base. In this next lesson on logarithmic expressions and equations, we will learn h…
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Problems 28
- Solve for xxx. ln(3x−7)=21.\ln(3x-7)=21.ln(3x−7)=21.
- Solve for xxx. 4lnx−ln2=84\ln x - \ln 2=84lnx−ln2=8
- What is the domain of f(x,y)=ln(x+y−1)f(x,y)=\ln(x+y-1)f(x,y)=ln(x+y−1)?
- Solve log2(log3(log5x)))=0\log_2(\log_3(\log_5 x)))= 0log2(log3(log5x)))=0.
- Solve the equation log2(x)+log2(3x)log2(6x)=1.\frac{\log_2 (x) + \log_2(3x)}{\log_2(6x)} = 1.log2(6x)log2(x)+log2(3x)=1.
- Find the value of xxx such that the difference between log2(x+3)\log_2 (x+3)log2(x+3) and log2x\log_2 xlog2x is 333.
- List all solutions to the equation 2logx=log(2x)2 \log x = \log (2x)2logx=log(2x).
- Solve the equation logx256=x\log_x 256 = xlogx256=x.
- If log6(x)+log6(4)=2\log_6(x) + \log_6(4) = 2log6(x)+log6(4)=2, find xxx.
- If 2=log6(x)2 = \log_6(x)2=log6(x), find xxx.
- Which values of xxx are solutions to this equation? x=log2(3x−1)x = \log_2(3x - 1)x=log2(3x−1)
- Solve for xxx: 4(log(4x+2))=log(x−6)+84(\mathrm{log}(4x+2))=\mathrm{log}(x-6)+84(log(4x+2))=log(x−6)+8
- When Justin goes outside again, how many years will have passed since last time?
- Find xxx:ln(x)=1\ln(x)=1ln(x)=1
- Solve for xxx: log3(7x+3)=log3(5x+9)\log_{3} (7x+3) = \log_{3} (5x+9)log3(7x+3)=log3(5x+9)
- Solve for xxx if log7(x−3)+log7(x+2)=log714\log_{7}(x-3) + \log_{7}(x+2) = \log_{7}14log7(x−3)+log7(x+2)=log714.
- Solve the logarithmic equation log2(x+2)+log2(3)=log2(27)\log_{2} (x+2) + \log_{2} (3) = \log_{2}(27)log2(x+2)+log2(3)=log2(27) for xxx.
- Solve: ln(x)=8\ln (x) = 8ln(x)=8
- Solve for xxx in the equation 2log(3x)=42\log(3x) = 42log(3x)=4.
- Solve for xxx: ln(x−3)+ln(x−2)=ln(2x+24)\ln (x-3) + \ln(x-2) = \ln (2x +24)ln(x−3)+ln(x−2)=ln(2x+24)
- Solve for xxx below. log4(x)−log4(x−1)=12\log_{4} (x) - \log_{4} (x-1) = \frac{ 1}{2}log4(x)−log4(x−1)=21
- Solve for xxx if 4+log3(2x+5)=64 + \log_{3} (2x +5) = 64+log3(2x+5)=6.
- Solve for xxx below. 2log9(x)−log9(6x−1)=02\log_{9}(\sqrt{x}) - \log_{9} (6x - 1) = 02log9(x)−log9(6x−1)=0
- Solve for xxx: logx+log(x−1)=log(3x+12)\log x + \log (x-1) = \log (3x +12)logx+log(x−1)=log(3x+12)
- Solve the logarithmic equation: log3(2x−7)+log32=2\log _{3} (2x-7)+\log_{3}2= 2log3(2x−7)+log32=2
- Solve for xxx: log3(1+log3(2x−7))=1\log_{3}(1+\log_{3}(2^{x}-7)) = 1log3(1+log3(2x−7))=1
- Solve for xxx: log3(x3+5)−log3(x+1)=4\log_{3}(x^{3}+5) - \log_{3}(x+1)= 4log3(x3+5)−log3(x+1)=4
- Solve the equation log2(x)+log2(x+3)=2\log_2(x) + \log_2(x + 3) = 2log2(x)+log2(x+3)=2.