The exponential equation out of the specified options that is equivalent to this logarithmic equation log x = 4 is given by: Option B: 10^4 = x
What is logarithm ?
When you raise a number with an exponent, there comes a result.
Lets say you get [tex]a^b = c[/tex]
Then, you can write 'b' in terms of 'a' and 'c' using logarithm as follows
[tex]b = \log_a(c)[/tex]
'a' is called base of this log function. We say that 'b' is the logarithm of 'c' to base 'a'
Log with base e = 2.71828... is written as [tex]\ln(x)[/tex] simply.
Log with base 10 is written as [tex]\log(x)[/tex] simply.
The given logarithmic equation is;
[tex]\log x = 4[/tex]
Since, log with base 10 is written as [tex]\log(x)[/tex] simply, therefore, we have:
[tex]\log_{10} x = 4[/tex]
Using the definition of logarithm, we get;
[tex]x = 10^4[/tex]
Equivalently, [tex]10^4 = x[/tex] (option B).
Thus, the exponential equation out of the specified options that is equivalent to this logarithmic equation log x = 4 is given by: Option B: 10^4 = x
Learn more about logarithm here:
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