Answer:
The equation is correct
Step-by-step explanation:
The equation, written as:
[log_2 (10)][log_4 (8)][log_10 (4)] = 3
Consider the change of base formula:
log_a (x) = [log_10 (x)]/ [log_10 (a)]
Applying the change of base formula to change the expressions in base 2 and base 4 to base 10.
(1)
log_2 (10) = [log_10 (10)]/[log_10 (2)]
= 1/[log_10 (2)]
(Because log_10 (10) = 1)
(2)
log_4 (8) = [log_10 (8)]/[log_10 (4)]
Now putting the values of these new logs in base 10 into the left-hand side of original equation to verify if we have 3, we have:
[log_10 (2)][log_8 (4)][log_10 (4)]
= [1/ log_10 (2)][log_10 (8) / log_10 (4)][log_10 (4)]
= [1/log_10 (2)] [log_10 (8)]
= [log_10 (8)]/[log_10 (2)]
= [log_10 (2³)]/[log_10 (2)]
Since log_b (a^x) = xlog_b (a)
= 3[log_10 (2)]/[log_10 (2)]
= 3 as required
Therefore, the left hand side of the equation is equal to the right hand side of the equation.
