Convert to an exponential equation.
log 11 = 1.0414
A 101.0414 = 11
B 111.0414 = 10
C 1.041410 = 11
D 1011 = 1.0414
10^1.0414 = 11
Using the definition of logarithms
y=loga(x) .......(1a) ≡ ay = x .............(1b)
Put x=11 in (1a), log(x) is understood to be base 10, so a=10, y=1.0414
[1a] 1.0414 = log10(11)
By the definition of logarithms, (1a) is equivalent to (1b), so substituting the same values,
[1b] 101.0414 = 11
You will find the above fit one of the answer choices on your screen or your book.
In the future, please use ^ to mean exponentiation, for example 2^(4x) to mean 24x.
To convert a logarithmic equation into an exponential equation, you need to understand the relationship between logarithms and exponentials.
In a logarithmic equation of the form log(base a) x = b, the base (a) and the logarithm result (b) tell you the exponent needed to raise the base (a) to obtain the value (x). So, in this case, we have:
log 11 = 1.0414
To rewrite this as an exponential equation, we can use the concept that the logarithm (1.0414) is the exponent that we need to raise the base (10) to obtain the result (11). Therefore, the exponential equation equivalent to the given logarithmic equation is:
10^1.0414 = 11
So the correct answer is option A: 101.0414 = 11.