Property 1
Exponential Function and Logarithm
Logarithmic function is the inverse exponential function.
Also exponential function is inverse logarithmic function.
\[a^x=y\iff x=\log_a y\]
Example
\(2^x=3\Rightarrow x=\log_2 3\)
\(5^x=7\Rightarrow x=\log_5 7\)
\(\log_2 x=3\Rightarrow x=2^3\)
\(\log_3 x=5\Rightarrow x=3^5\)
1.
\(2^x=5\)
\(\Rightarrow x=?\)
2.
\(5^x=3\)
\(\Rightarrow x=?\)
3.
\(2^{x+1}=3\)
\(\Rightarrow x=?\)
4.
\(3^{x-1}=8\)
\(\Rightarrow x=?\)
5.
\(3^{-x}=5\)
\(\Rightarrow x=?\)
6.
\(7^{1-x}=2\)
\(\Rightarrow x=?\)
7.
\(5^{x+2}=50\)
\(\Rightarrow x=?\)
8.
\(7^{x-1}=3\)
\(\Rightarrow x=?\)
9.
\(\log_2 x=3\)
\(\Rightarrow x=?\)
10.
\(\log_3 x=1\)
\(\Rightarrow x=?\)
11.
\(\log_6 x+2=0\)
\(\Rightarrow x=?\)
12.
\(\log_{1/3}27=x\)
\(\Rightarrow x=?\)
13.
\(\log_3(\log_4x)=1\)
\(\Rightarrow x=?\)
14.
\(\log_4(1+\log_2(x-2))=1\)
\(\Rightarrow x=?\)