# Logarithms

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Problem #1
What is the value of $\log_{\frac{1}{4}} 8\sqrt[3]{2}$?

Problem #2
What is the value of $\log_4 \sqrt{2} +\log_{\sqrt{8}} 2$?

Problem #3
$3^{\log_3 1}+x^{\log_4 2} =3$
Find $x$?

Problem #4
Let $9^x=3\sqrt{3}$
What is the value of $\log_2 (1-x)$?

Problem #5
$\log_{15} 2 = \alpha$ and $\log_{15} 3= \beta$
What is the value of $\log_{\sqrt{15}} 100$?

Problem #6
$\log_{10} (x^2-9)=\log_{10} (x+3) +2 \log_{10} 3$
What is the value of $x$?

Problem #7
$\log_x (2x-3)+\log_x 3=2$
What is the value of $\log_8 (x^2+6.5)$?

Problem #8
$\log_{10} (x^2-11)=1+\log_{10} x$
What is the value of $\log_{10} (x-1)$?

Problem #9
$\log_3 x +\log_x 9 =3$
What is the value of $\log_{\sqrt{3}} x$?

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