Question

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

Answer 1

The answer is b on edj.

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

Answer 2

The equation is correct

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