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log₄x+log₅(x-6)=2

\(x\approx 8.179270752839169853762493233675433392045\dots\)

What system?

X marks the spot  - on a treasure map.   :)

How do I distribute the x on the outside to the numbers in the parentheses?

x(x+5)(x+5) 

\(x(x+5)(x+5) \\ x\times (x+5)(x+5) =x\times(x^2+10x+25)=x^3+10x^2+25x\\ or\\ x(x+5)\times (x+5)=(x^2+5x)(x+5)=x^3+5x^2+5x^2+25x=x^3+10x^2+25x\)

The sum of the angle measures of a polygon with n sides is 1260.

Find n.

\(\begin{array}{|rcll|} \hline (n-2)\cdot 180 &=& 1260 \quad &| \quad : 180 \\ n-2 &=& \frac{1260}{180} \\ n-2 &=& 7 \quad &| \quad +2 \\ \mathbf{n} & \mathbf{=} & \mathbf{9} \\ \hline \end{array}\)

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What is the square root of 98.38?

\(\sqrt{98.38}=9.91866926558 \)     !

x^2=27

\(x^2=27\)

\(x=\pm\sqrt{27}\)

\(x_1=5.19615242271\ \ x_2=-5.19615242271\)

  !

log(3x-9)=log(2x+6)

\(\begin{array}{|rcll|} \hline \log(3x-9)&=& \log(2x+6) \\ 3x-9 &=& 2x+6 \quad &| \quad -2x \\ x -9 &=& 6 \quad &| \quad +9 \\ x &=& 15 \\ \hline \end{array}\)

Solve for x:
log(3 x - 9) = log(2 x + 6)

Subtract log(2 x + 6) from both sides:
log(3 x - 9) - log(2 x + 6) = 0

log(3 x - 9) - log(2 x + 6) = log(1/(2 x + 6)) + log(3 x - 9) = log((3 x - 9)/(2 x + 6)):
log((3 x - 9)/(2 x + 6)) = 0

Cancel logarithms by taking exp of both sides:
(3 x - 9)/(2 x + 6) = 1

Multiply both sides by 2 x + 6:
3 x - 9 = 2 x + 6

Subtract 2 x - 9 from both sides:
Answer: |x = 15

Using Newton-Raphson method:

x ≈ 8.17927

2x+y=9

x=12-3y

2(12-3y)+y=9

24-6y+y=9

24-5y=9

x=3

y=3

(3,3)

true because ur given 36 extra minutes which gives you the time to go at a faster rate, but at a slower rate but it depends so it could be either one

UMM this is really easy but just collect like terms... 5x = 6 then do x = 6/5 smh

(32a) / (8a²)     =     (32/8) · (a/a²)     =     (4) · (1/a)  =  4/a

ln(x) + ln(4x)  =  2

          ln(4x²)  =  2                                 (adding logs  --->  multiplying numbers)

                4x²  =  e²                               (raise both sides to the power of e)

                  x²  =  e² / 4                           

                    x  =  e/2