Question

Solve log8 12=x-2. Round your answer to four decimal places.

Answer 1

B

Explanation:

edge 2020

Answer 2

`\large\boxed{x\approx3.1950}`

Explanation:

`\log_ab=c\iff a^c=b\\\\\log_812=x-2\iff8^(x-2)=12\\\\(2^3)^(x-2)=4\cdot3\qquad\text{use}\ (a^n)^m=a^(nm)\\\\2^(3(x-2))=2^2\cdot3\qquad\text{use the distributive property}\\\\2^(3x-6)=2^2\cdot3\qquad\text{divide both sides by}\ 2^2\\\\(2^(3x-6))/(2^2)=3\qquad\text{use}\ (a^n)/(a^m)=a^(n-m)\\\\2^(3x-6-2)=3\\\\2^(3x-8)=3\qquad\text{logarithm of both sides}\\\\\log_22^(3x-8)=\log_23\qquad\text{use}\ \log_aa^n=n\\\\3x-8=\log_23\qquad\text{add 8 to both sides}`

`3x=\log_23+8\qquad\text{divide both sides by 3}\\\\x=(\log_23+8)/(3)\\\\\log_23\approx1.5849625\\\\x\approx(1.5849625+8)/(3)\approx3.1950`