Question

Solve the following log for x.

Answer 1

\[\log _{64}25x-\log _{64}x-7=2/3\]

Answer 2

My choices are (A) x=9/24,(B) x=-112/9,(C) -487/3,582, and (D) no solution. I'm pretty sure the answer is B, but I just want to make sure that I'm correct.

Answer 3

is it \[\log(25x)-\log(x-7)=\frac{2}{3}\]?

Answer 4

No, its, \[\log _{64}25x-\log_{64}(x-7)=2/3\]

Answer 5

it's*

Answer 6

yea ok start with \[\log_{64}(\frac{25x}{x-7})=\frac{2}{3}\] then write in exponential form

Answer 7

i.e. \[\frac{25x}{x-7}=64^{\frac{2}{3}}\]

Answer 8

Okay... Now what? @satellite73

Answer 9

you know what \[\sqrt[3]{64^2}\] is ?

Answer 10

That is equal to 16

Answer 11

oh doh, you already said B
either it was a lucky guess, or you did it correctly

Answer 12

yeah if you solve \[\frac{25x}{x-7}=16\] you get \[-\frac{112}{9}\]

Answer 13

Okay, thanks for confirming. I thought that was correct but I just wanted to double check. @satellite73

Answer 14

your welcome (you did all the work)