Question

solve for X. log(base3)x^2=2log(base3)4-4log(base3)5

Answer 1

like this?
\[\log_3(x^2) = 2\log_3(4)-4\log_3(5)\]

Answer 2

log_3(x^2)=2log_3(4)-4log_3(5)??????

Answer 3

x^2 = 3^RHS
x = sqrt(3^RHS)

I think?

Answer 4

x = 0.16

Answer 5

since it is all base three, lets simplify each side down to one log. The left side is already done. On the right side we have:
\[2\log_3 (4)-4\log_3(5) = \log_3(4^2)-\log_3(5^4) = \log_3\left(\frac{16}{625}\right)\]
So now we have:
\[\log_3(x^2) = \log_3\left(\frac{16}{625}\right) \iff x^2 = \frac{16}{625} x = \pm \frac{4}{25}\]

Answer 6

whoops there should be an arrow in between the fraction 16/625 and x in the last line.