Answer:
x = 3.1
Step-by-step explanation:
[tex] {10}^{x} = 1200[/tex]
To solve first take logarithm to both sides
That's
[tex] log_{10}(10) ^{x} = log_{10}(1200) [/tex]
[tex] log_{10}(10)^{x} = x log_{10}(10) [/tex]
But
[tex] log_{10}(10) = 1[/tex]
So we have
[tex]x = log_{10}(1200) [/tex]
Write 1200 as a number with the factor 100
That's
1200 = 100 × 12
So we have
[tex]x = log_{10}(100 \times 12) [/tex]
Using the rules of logarithms
That's
[tex] log_{a}(x \times y) = log_{a}(x) + log_{a}(y) [/tex]
Rewrite the expression
That's
[tex]x = log_{10}(100) + log_{10}(12) [/tex]
[tex]x = log_{10}(10)^{2} + log_{10}(12) [/tex]
[tex]x = 2 log_{10}(10) + log_{10}(12) [/tex]
[tex] log_{10}(10) = 1[/tex]
[tex]x = 2 + log_{10}(12) [/tex]
x = 3.079
So we have the final answer as
x = 3.1 to one decimal place
Hope this helps you
