Question

I need to know how to answer this question step by step. I need to be able to explain it. How do we know if we use the equation A(t) = a (1 + r)^t and when we use A=Pe^rt when calculating exponential growth or decay?

Answer 1

The given is

$\text{log}_864$

This can be rewritten as follows:

$\text{log}_864=x$

Recall that in exponential form using the logarithmic,

$\log _by=x$

If band x are positive real numbers and b is not equal to 1 then, then

$\log _by=x\text{ is equivalent to }b^x=y\text{.}$

From the comparing

$\text{Comparing log}_864=x\text{ and log}_by=x$

We get b=8 and y=64.

$\text{Substitute b=8 and y=64 in }b^x=y\text{ as follows:}$$8^x=64$

$8^x=8^2$$We\text{ know that if }a^n=a^m\text{ implies that n=m.}$$we\text{ have }8^x=8^2\text{ it implies that x=2}$

Hence we get

$\text{log}_864=2$