Solve the equation lgx=−17
This question bothers me, cause its supposed to be higher level but I'm confused here if lg is maybe log or if its asking for three numbers that equate to -17.
I suspect it is
Logx=-17
Since there is no base assume it is in base 10
X=10^(-17)
Or
X=1×10^(-17)
lg x is encountered in computing theory, and usually denotes log base 2.
lg x = -17
x = 2^-17
Wolfram explains that in German and Russian notations, the notation lgx is used to mean the common logarithm log10 x
so it could just mean log x=−17
or
x = 10^-17
oobleck's take is the more likely
The equation you have given is of logarithmic form, where "lg" represents the base-10 logarithm (common logarithm). The goal is to solve for the value of "x" that satisfies the equation lg(x) = -17.
To solve this equation, we need to rewrite it in exponential form. In general, the logarithmic form log(base b)(x) = y is equivalent to the exponential form b^y = x.
Applying this concept, we can rewrite lg(x) = -17 in exponential form as 10^(-17) = x.
Now, we can evaluate the exponential expression using a calculator or by breaking it down.
Using a calculator:
10^(-17) = 1.0 × 10^(-17) ≈ 1.0 × 10^(-17) ≈ 0.00000000000000001
Therefore, the solution to the equation lg(x) = -17 is x ≈ 0.00000000000000001.
Please note that this solution assumes we are working with real numbers. If this equation is part of a complex logarithmic problem or if you are looking for solutions within a specific domain, please provide more context.