Mister Exam

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log(1/9)(5-x)=-2 equation

The teacher will be very surprised to see your correct solution 😉

You have entered [src]

log(1/9)*(5 - x) = -2

\left(5 - x\right) \log{\left(\frac{1}{9} \right)} = -2

Simplify

Detail solution

Given the equation:

log(1/9)*(5-x) = -2

Expand expressions:

-10*log(3) + 2*x*log(3) = -2

Reducing, you get:

2 - 10*log(3) + 2*x*log(3) = 0

Expand brackets in the left part

2 - 10*log3 + 2*x*log3 = 0

Move free summands (without x)
from left part to right part, we given:

2 x \log{\left(3 \right)} - 10 \log{\left(3 \right)} = -2

Divide both parts of the equation by (-10*log(3) + 2*x*log(3))/x

x = -2 / ((-10*log(3) + 2*x*log(3))/x)

We get the answer: x = (-1 + log(243))/log(3)

The graph

Plot the graph f1(x)

Plot the graph f2(x)

Sum and product of roots [src]

sum

-2 + log(59049)
---------------
     log(9)

\frac{-2 + \log{\left(59049 \right)}}{\log{\left(9 \right)}}

-2 + log(59049)
---------------
     log(9)

\frac{-2 + \log{\left(59049 \right)}}{\log{\left(9 \right)}}

product

-2 + log(59049)
---------------
     log(9)

\frac{-2 + \log{\left(59049 \right)}}{\log{\left(9 \right)}}

-2 + log(59049)
---------------
     log(9)

\frac{-2 + \log{\left(59049 \right)}}{\log{\left(9 \right)}}

(-2 + log(59049))/log(9)

Rapid solution [src]

     -2 + log(59049)
x1 = ---------------
          log(9)

x_{1} = \frac{-2 + \log{\left(59049 \right)}}{\log{\left(9 \right)}}

x1 = (-2 + log(59049))/log(9)

Numerical answer [src]

x1 = 4.08976077337316

x1 = 4.08976077337316