Laws of Logarithms
Evaluate: without using a calculator, except for the first one. The 5.6 is supposed to be subscript, but i don't know how to make it small.
4log(5.6)84
log84/log5.6
Do I multiply this by four or something? both of the logs?
One major rule of logs, used when changing bases is
log ba
= log a / log b
so 4 log 5.684
= 4(log 84 / log 5.6)
= 4(1.924279.../.74818..) = 10.2877
Thanks very much Reiny :)
To evaluate the given expressions without using a calculator, let's break them down step by step.
1. 4log(5.6)84:
This expression indicates that we need to apply the logarithm to the number 84, with a base of 5.6. Since you mentioned using a calculator, I assume you know the value of log(5.6). Let's assume it is x for now.
The expression can then be rewritten as 4 * x * 84.
So, if you know the value of log(5.6), you can substitute it into the expression and calculate the result.
2. log84/log5.6:
This expression involves two logarithms, log(84) and log(5.6), and requires the quotient rule of logarithms.
According to the quotient rule:
log(a/b) = log(a) - log(b)
So, using this rule, we can rewrite the expression as log(84) - log(5.6).
Now, if you know the values of both log(84) and log(5.6), you can substitute them into the expression and calculate the result.
Please note that without knowing the specific values of log(5.6) or log(84), it is not possible to determine the exact values numerically.