Question

log(2x-5)+log(x-6) = log(6x+20) a. 11 b. 9 c. 13 d. 7

Answer 1

Answer:

11 is the answer

Hope this will help you

Answer 2

Answer:

$\Large\boxed{X=\frac{23+\sqrt{449}}{4}=11.0}$

Step-by-step explanation:

Given:

log(2x-5)+log(x-6) = log(6x+20)

To solve this problem, first you have to use the log formula from left to right numbers.

Solutions:

log₁₀(2x-5)+log₁₀(x-6)=log₁₀(6x+20)

First, you have to use the log rule or log formula.

$\Large\boxed{\textnormal{LOG RULE AND LOG FORMULA}}$

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

$\displaystyle \log _{10} (2x-5)++\log _{10}(x-6)=\log _{10}((2x-5)(x-6))$

$\displaystyle \log _{10}\left(\left(2x-5\right)\left(x-6\right)\right)=\log _{10}\left(6x+20\right)$

$\displaystyle \log _b\quad  f(x)=\log_b(g(x)) \quad f(x)=g(x)$

$\displaystyle (2x-5)(x-6)=6x+20$

Solve. (Simplify.)

$\left(2x-5\right)\left(x-6\right)=6x+20=2x^2-17x+30=6x+20$

Subtract by 20 from both sides.

$\displaystyle 2x^2-17x+30-20=6x+20-20$

Solve.

$\displaystyle 2x^2-17x+10=6x$

Then, you subtract by 6x from both sides.

$\displaystyle 2x^2-17x+10-6x=6x-6x$

Solve.

$\displaystyle 2x^2-23x+10=0$

A=2

B=(-23)

C=10

$\displaystyle \frac{-\left(-23\right)+\sqrt{\left(-23\right)^2-4\* \:2* \:10}}{2* \:2}=\boxed{\frac{23+\sqrt{449}}{4}}$

$\displaystyle x=\frac{23+\sqrt{449}}{4},x=\frac{23-\sqrt{449}}{4}$

$\Large\boxed{X=\frac{23+\sqrt{449} }{4}=11.0 }$

In conclusion, the correct answer is x=23√449/4=11.0.