Question

log 8 + log 25 + 2 log 3 - log 18​

Answer 1

Answer:

$\Large\boxed{2}$

Step-by-step explanation:

To solve this problem, first you have to used log formula.

Given:

log 8+ log 25+2 log 3- log 18

Solutions:

Used log rules.

$\Large\boxed{\textnormal{LOG RULES FORMULA}}$

$\displaystyle \log _c\left(a\right)+\log _c\left(b\right)=\log _c\left(ab\right)$

$\displaystyle\log _{10}\left(8\right)+\log _{10}\left(25\right)=\log _{10}\left(8\cdot \:25\right)$

$\displaystyle \log _{10}\left(8\cdot \:25\right)+2\log _{10}\left(3\right)-\log _{10}\left(18\right)$

Multiply the numbers from left to right.

$\displaystyle 8*25=200$

$\displaystyle \log _{10}\left(200\right)+2\log _{10}\left(3\right)-\log _{10}\left(18\right)$

$\Large\boxed{{a\log _c\left(b\right)=\log _c\left(b^a\right)}}$

$\displaystyle 2\log _{10}\left(3\right)=\log _{10}\left(3^2\right)$

$\displaystyle \log _{10}(200)+\log _{10}\(3^2)-\log _{10}(18)$

$\displaystyle \log _{10}\left(200\right)+\log _{10}\left(3^2\right)=\log _{10}\left(3^2\cdot \:200\right)$

$\displaystyle \log _{10}\left(3^2\cdot \:200\right)-\log _{10}\left(18\right)$

Solve.

Multiply.

$\displaystyle 3^2*200=1800$

$\displaystyle \log _{10}\left(1800\right)-\log _{10}\left(18\right)$

$\displaystyle \log _{10}\left(\frac{1800}{18}\right)$

Divide.

$\displaystyle 1800\div18=100$

$\log _{10}\left(100\right)$

$\displaystyle 10^2=10*10=100$

$\displaystyle \log _{10}\left(10^2\right)$

$\displaystyle \log _{10}\left(10^2\right)=2\log _{10}\left(10\right)$

$\displaystyle 2\log _{10}\left(10\right)$

$\displaystyle \log _{10}\left(10\right)=1$

Multiply the numbers from left to right.

$\displaystyle 2*1=\boxed{2}$

Hence, the correct answer is 2.

Answer 2

Answer:

Step-by-step explanation: