Question

Help! Logarithmic functions

Answer 1

im saying use the definition of the logarithm to rearrange the equation and solve for x

Answer 2

\[\log_{3}(3) + \log_3(x) = 5\\ \log_{3}(3x) = 5 \\ 3^5 = 3x \\ \frac{3^5}{3} = x \\ 3^4 = x \\ 81 = x\]

Answer 3

Yes, I'm here :)

Answer 4

If you have any questions, let me know

Answer 5

you had reached \[\log_3 x=4\]already,
now
applying the definition of the logarithm

\[\log_3 x=4\qquad\Rightarrow\qquad x=3^{4}\]\[\qquad\qquad\qquad \qquad \qquad \quad=3\times3\times3\times3\]

Answer 6

81

Answer 7

yep

Answer 8

@Hero, your amazing, by the way! Oh, and Thanks so much @UnkleRhaukus
I really, sincerely, appreciate the help from both of you!

Answer 9

if you wanted to check your solution \(x=3^4=81\)
just plug into
\[\log_{3}(3) + \log_3(x) = 5\]
see get
\[\log_{3}(3) + \log_3(3^4) = 5\]\[\log_{3}(3) + 4\log_3(3) = 5\]\[\qquad\qquad\quad1+4=5\]