yasminothman020 yasminothman020
  • 12-10-2018
  • Mathematics
contestada

4. Use the change of base rule to find the logarithm to four decimal places. (2 points) log base eight of 0.082.
A) -0.8314
B) 97.5610
C) -1.0862
D) -1.2027

Respuesta :

InesWalston
InesWalston InesWalston
  • 22-10-2018

Answer-

Using the change of base rule, the value of  [tex]\log_8 0.082[/tex]  was found to be -1.2027

Solution-

Change of base rule,

[tex]\log_y x=\frac{\log_a x}{\log_a y}[/tex]

where, a is the new base.

Here,

x = 0.082 and y = 8

Taking a=10 in this case,

[tex]\log_8 0.082=\frac{\log_10 0.082}{\log_10 8}[/tex]

[tex]=\frac{-1.0861}{0.9030}[/tex]

[tex]=-1.2027[/tex]

The value of 'a' really does not matter. Taking different bases will yield the same result, because at the end we are taking the ratio.  

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