Question #190022

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

(0.167, -1)

(1,0)

(6,1)

(36,2)


1
Expert's answer
2021-05-12T06:50:20-0400

y=logbase(x)y=log_{base}(x)

(a)

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

base1=0.167base^{-1}=0.167

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

base=10.167base=\frac{1}{0.167}

base5.98base\approx5.98

therefore the logarithmic equation is:

y=log5.98(x)y=log_{5.98}(x)


(b)

0=logbase(1)0=log_{base}(1)

base0=1...There will be an infinite solution for the basebase^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)y=log(X)


(c)

1=logbase(6)base1=6base=61=log_{base}(6)\\base^1=6\\base=6

Therefore the logarithmic equation is:

y=log6(x)y=log_6(x)


(d)

2=logbase(36)base2=36base=62=log_{base}(36)\\base^2=36\\base=6

Therefore the logarithmic equation is:

y=log6(x)y=log_6(x)


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