Question

which of the following expressions is equivalent to log8(m)/log(m). your options are: log(8), 1/log(8), log(m), and log8(8). please show your work, which will require the generalized log rule logb(a)=logx(a)/logx(b) (change of base rule)

Answer 1

Using the change of base rule, log8(m)/log(m) simplifies to log(m)/log(8), which is further equivalent to log8(m), and the final equivalent expression is log(8).

Step-by-step explanation:

To find which expression is equivalent to log8(m)/log(m), we use the change of base rule for logarithms, which is logb(a) = logx(a)/logx(b). By applying this rule, we can rewrite the given expression as:

log8(m)/log(m) = log(m)/log(8).

Now, using the property of logarithms that states the logarithm of a number resulting from the division of two numbers is the difference between the logarithms of the two numbers, we get:

log(m)/log(8) = log8(m).

Here, log8(m) is the power to which 8 must be raised to equal m, which is the base 8 logarithm of m. Finally, we can conclude that the original expression is equivalent to log(8).