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
