Answer:
x = 50
Step-by-step explanation:
[tex] log_{10}(2x) = 2[/tex]
Use the following property.
[tex] log_{a}(m) = n \\ {a}^{n} = m[/tex]
[tex] {10}^{2} = 2x \\ 100 = 2x \\ \frac{100}{2} = x \\ 50 = x[/tex]
Therefore, the value of x is 50.
Answer Check
Substitute x = 50 in the equation.
[tex] log_{10}(2x) = 2 \\ log_{10}(2(50)) = 2 \\ log_{10}(100) = 2 \\ {10}^{2} = 100 \\ 100 = 100[/tex]
The equation is true. Therefore x = 50.
Note
If you don't write logarithm with base, it is classified as common logarithm or base 10.
