Question

How do I solve 4.258^9t = 8 ??

Answer 1

First, some clarification. What do you mean by "^9t"? If the entire "9t" is to be used as your exponent, you should enclose "9t) in parentheses for added clarity.

Answer 2

@mathmale I meant 9t)

Answer 3

(9t)? 9t) has no meaning.

Answer 4

(9t)

Answer 5

4.258^(9t)=8 is an exponential equation because of that "^(9t)."

Answer 6

Your job is to solve this equation first for (9t) and then, secondly, for (t).

Which mathematical operation pairs with exponentiation?

Answer 7

Have you seen the following before?\[\log a^b =b \log a\]

Answer 8

yes!

Answer 9

Your 4.258^(9t)=8 has pretty much the same form as a^b=c.

So, which math op must you use at this point, to eliminate the exponentiation from your equation?

Answer 10

Reminder: Given\[a^b=c,\]

Answer 11

\[\log a^b = \log c\]

Answer 12

The math function that "undoes" the exponential function is the _______ function.

I need to get off the 'Net now, but will be back at about 6. See what you can do with the hints I've given you so far. Find 9t first, and then find t. Then you'll be done.

Answer 13

Still there? I'm back.

Answer 14

how do i find 9t

Answer 15

\[4.258^{9t} = 8\iff \frac{\ln(8)}{\ln(4.258)}=9t\]

Answer 16

so rounding my answer to the third decimal, it would be 1.435

Answer 17

This outcome is a correct application of the info I shared with you earlier:

Have you seen the following before?
\[\log a^b=b \log a\]

Answer 18

Please check your answer by substituting your 1.435 for t in the original equation. Is the equation then true? or not?

Answer 19

4.258^9t = 8 ??\[ 4.258^{9(1.435)} = 8 ??\]

Answer 20

Here you MUST multiply 9 and 1.435 together first to obtain the exponent of base 4.258.