Log of a Power
Read this topicExplanations 3
- The power rule for logarithms states that logb(AC)=C⋅logbA\log_b(A^C) = C\cdot \log_bAlogb(AC)=C⋅logbA Proof: bC⋅logbA=blogbA⋅C=(blogbA)C=AC=blogb(AC).b^ {C\cdot \log_bA…
By Benjamin Qi
- (Video) Power Rule of Logarithms by SnugglyHappyMathTime Check out this video by SnugglyHappyMathTime to learn about the power rule!
By Trisha, Anusha Rahman
- Log of a Power A logarithm is the inverse function of an exponential function. That means that if bx=ab^x=abx=a, then logb(a)=xlog_b(a)=xlogb(a)=x. In other words, a logarithm …
By Trisha, Anusha Rahman
Problems 14
- Find the product of all real roots of the equation xlog10x=10x^{\log_{10} x} = 10xlog10x=10. Source: Alex Zhu, Problems of the Week 2, 2012
- Compute log96log35.\frac{\log 9^6}{\log 3^5}.log35log96.
- Let x=4/253x = \sqrt[3]{4/25}x=34/25. There is a unique value of yyy such that 0<y<x0 < y < x0<y<x and xx=yyx^x = y^yxx=yy. What is the value of y3y^3y3? (Hint: Let k∈(0,1)k\in…
- 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…
- If x>10x > 10x>10, what is the greatest possible value of the expression (logx)logloglogx−(loglogx)loglogx?{( \log x )}^{\log \log \log x} - {(\log \log x)}^{\log \log x…
- What is 2⋅log4(8)2 \cdot \log_4(8)2⋅log4(8)?
- What can xxx be? Select all solutions. 2ln(x+5)=ln1002\ln(x+5)=\ln1002ln(x+5)=ln100
- Simplify the expression: log3(3x⋅9x100)\log_{3}(3^x \cdot 9x^{100})log3(3x⋅9x100)
- Solve for xxx: 2(x+1)=1032^{(x+1)}= 10^{3}2(x+1)=103
- Use the log of a power rule to rewrite log2(4⋅8)\log_{2}(4 \cdot 8)log2(4⋅8)
- Use the log of a power rule to simplify log394\log_{3}9^{4}log394
- Use the properties of logarithms to rewrite log464x\log_{4}64^{x}log464x
- Simplify this logarithm: log39x\log_{3} 9^{x}log39x
- Evaluate: log28+log24\log_{2}8 + \log_{2}4log28+log24