Algebra

Logarithmic Functions

Logarithmic Functions: Level 1 Challenges

         

log735+log735log725= ? \large \log_7 35 + \log_7 35 - \log_7 25 = \ ?

logyx+logxy=2\large\log_{\color{#20A900}{y}}{\color{#3D99F6}{x}}+\log_{\color{#3D99F6}{x}}{\color{#20A900}{y}}=-2 Find the value of xy.\color{#3D99F6}{x}\color{#20A900}{y}.

If 4log12(x9)+log12(x6)=126 4 \log_{12} \left(x^9\right) + \log_{12} \left(x^6\right) = 126, find x.x.

1log2100!+1log3100!+1log4100!++1log100100!= ?\frac{1}{\log_{2}{100!}}+\frac{1}{\log_{3}{100!}}+\frac{1}{\log_{4}{100!}}+\ldots+\frac{1}{\log_{100}{100!}}= \ ?

Find the smallest number among the following numbers:

(A) log20152016\log_{2015}2016

(B) log20162017\log_{2016}2017

(C) log20172018\log_{2017}2018

(D) log20182019\log_{2018}2019

(E) log20192020\log_{2019}2020

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