Answer to Question #190022 in Algebra for will

Question

Write the log equation for these coordinates: y= log_base(x)

(0.167, -1)

(1,0)

(6,1)

(36,2)

Answer 1

$y=log_{base}(x)$

(a)

$-1=log_{base}(0.167)$

$base^{-1}=0.167$

$\frac{1}{base}=0.167$

$base=\frac{1}{0.167}$

$base\approx5.98$

therefore the logarithmic equation is:

$y=log_{5.98}(x)$

(b)

$0=log_{base}(1)$

$base^0=1...There\space will\space be\space an\space infinite\space solution\space for\space the\space base$

so, the base can be any number except 1 and negative numbers

in general, we can write,

$y=log(X)$

(c)

$1=log_{base}(6)\\base^1=6\\base=6$

Therefore the logarithmic equation is:

$y=log_6(x)$

(d)

$2=log_{base}(36)\\base^2=36\\base=6$

Therefore the logarithmic equation is:

$y=log_6(x)$