Logarithms

Complete the test and get an award.

Problem #1
What is the value of [tex] \log_3 243 [/tex]?

Problem #2
If [tex] \log_2 a=b [/tex], then what is the relation between [tex] a [/tex] and [tex] b [/tex]?

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

Problem #4
[tex] \log_{10} 2x =1[/tex]
Find [tex]\log_2(x+3)[/tex]

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

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

Problem #7
What is the value of [tex] \log_3 7 +\log_3 63 -\log_3 49 [/tex]?

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

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

Problem #10
Which one is correct?

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




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