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den301095 [7]
3 years ago
5

A teacher used the change of base formula to determine whether the equation below is correct. (log2 10)(log4 8)(log10 4)=3

Mathematics
2 answers:
Misha Larkins [42]3 years ago
7 0

Answer:

The equation is correct

Step-by-step explanation:

(log2 10)(log4 8)(log10 4)=3

Change of base formula

logb (x) = log10 (x)/ log10 (b)


Lets change all non base 10 logs to base 10 logs

(log2 10) = log10 (10)/ log10 (2)  

We know that log10 (10 ) = 1  so

(log2 10) = 1/ log10 (2)

(log4 8)  = log10 (8)/ log10 (4)

Now we can rewrite the original equation in all base 10

(log2 10)(log4 8)(log10 4)=3

1/ log10 (2) *  log10 (8)/ log10 (4) *  (log10 4)=3

I can cancel the log10 (4)/ log10 (4)

1/ log10 (2) *  log10 (8)=3

log10 (8)/ log10 (2)

We know that 8 = 2^3

log10 (2^3)/ log10 (2) =3

Remember  log a^b  = b * log a

3 * log10 (2) / log10 (2) =3

We can cancel log 10 (2)/ log10 (2)

3=3


The equation is correct


Inessa05 [86]3 years ago
3 0

Answer:

The answer is <u>b</u> on edj.

This is for those who don't want to read but credit goes to Wegnerkolmp2741o for solving the equation.

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