# Logarithms

Complete the test and get an award.

Problem #1
What is the value of $\log_3 243$?

Problem #2
If $\log_2 a=b$, then what is the relation between $a$ and $b$?

Problem #3
What is the value of $\log_{\frac{1}{2}} 4 +\log_5 {\frac{1}{5}}$?

Problem #4
$\log_{10} 2x =1$
Find $\log_2(x+3)$

Problem #5
If $\log_{10} 2x =1$, then what is the value of $\log_2 {(x+3)}$?

Problem #6
$\log_3 {\frac{x}{2}} -\log_3 2=-\log_{\frac{1}{3}} 9$
What is the value of $x$?

Problem #7
What is the value of $\log_3 7 +\log_3 63 -\log_3 49$?

Problem #8
$\log_{10} 2=0.3$ and $\log_{10} 3=0.48$
What is the value of $\log_{10} 36$?

Problem #9
If $\log_{10} 2 =b$, then what is the value of $2^{\log_{10} x}$?

Problem #10
Which one is correct?

Problem #11
$\log_b a=\frac{2}{3}$
What is the value of $\log_a b$?

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