The required solution for the expression is [tex]x = ln7/(10*ln2)[/tex]. Option D is correct
To solve [tex]2800 = 400.2^{10x}[/tex] for x.
what is an exponential function?
The function which is in format f(x) = [tex]a^x[/tex] where, a is constant and x is variable, the domain of this exponential function lies (-∞, ∞).
[tex]2800 = 400.2^{10x}[/tex]
[tex]2800/400= 2^{10x}[/tex]
[tex]7=2^{10x}[/tex]
taking log on both sides.
[tex]log_27=10x\\x=log_27/10\\x = log_e7/(10*log_e2)\\x =ln7/(ln2*10)[/tex]
(By properties of logarithm log can be separated to common base e)
The required solution for the expression is [tex]x = ln7/(10*ln2)[/tex].
Learn more about exponential function here:
brainly.com/question/15352175
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