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**tecktonikk** 1. If log_a X=2, what is log_a (1/x) ?

$\displaystyle \textcolor{red}{\log_a{x} = -\log_a\left(\frac{1}{x}\right)}$

2. Evaluate log_2 4 + log_4 8 + log_8 16 + log_16 32 + log_32 64 + log64 128

change of base formula, for example ...

$\displaystyle \textcolor{red}{\log_4(8) = \frac{\log_2(8)}{\log_2(4)}}$

3. Simpilfy Expression :

x= (log_10 11)(log_11 12)....(log_98 99)(log_99 100)

again, use the change of base formula ...

$\displaystyle \textcolor{red}{\log_{11}(12) = \frac{\log_{10}(12)}{\log_{10}(11)}} $

4. log_2 3√ 16

(the 3 is a script, not 3√ 16)

hint ... $\displaystyle \textcolor{red}{\sqrt[3]{16} = \sqrt[3]{2^4} = 2^{\frac{4}{3}}}$

5. (√ x) ^ log_x 2

two hints ... $\displaystyle \textcolor{red}{\sqrt{x} = x^{\frac{1}{2}}}$

$\displaystyle \textcolor{red}{x^{\log_x{2}} = 2}$