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Equation:
Equation x^3-27=0
Equation -x=6-7(x-3)
Equation 1/(6-y)-1/y-1/4=0
Equation log(x)=x-5
Express {x} in terms of y where:
-19*x+16*y=-9
-5*x+1*y=19
-1*x-15*y=13
7*x-19*y=17
Identical expressions
zero , eight ^x= five ^ one -2x
0,008 to the power of x equally 5 to the power of 1 minus 2x
zero , eight to the power of x equally five to the power of one minus 2x
0,008x=51-2x
Similar expressions
0,008^x=5^1+2x

0,008^x=5^1-2x equation

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

The solution

You have entered [src]

   -x          
125   = 5 - 2*x

\left(\frac{1}{125}\right)^{x} = 5 - 2 x

Simplify

The graph

Plot the graph f1(x)

Plot the graph f2(x)

Rapid solution [src]

        /    /     ___\\                   
        |    | 3*\/ 5 ||                   
        |    | -------||                   
        |    |  781250||                   
     2*W\-log\5       // + log(30517578125)
x1 = --------------------------------------
                    6*log(5)

x_{1} = \frac{2 W\left(- \log{\left(5^{\frac{3 \sqrt{5}}{781250}} \right)}\right) + \log{\left(30517578125 \right)}}{6 \log{\left(5 \right)}}

        /    /     ___\    \                   
        |    | 3*\/ 5 |    |                   
        |    | -------|    |                   
        |    |  781250|    |                   
     2*W\-log\5       /, -1/ + log(30517578125)
x2 = ------------------------------------------
                      6*log(5)

x_{2} = \frac{2 W_{-1}\left(- \log{\left(5^{\frac{3 \sqrt{5}}{781250}} \right)}\right) + \log{\left(30517578125 \right)}}{6 \log{\left(5 \right)}}

x2 = (2*LambertW(-log(5^(3*sqrt(5)/781250), -1) + log(30517578125))/(6*log(5)))

Sum and product of roots [src]

sum

   /    /     ___\\                         /    /     ___\    \                   
   |    | 3*\/ 5 ||                         |    | 3*\/ 5 |    |                   
   |    | -------||                         |    | -------|    |                   
   |    |  781250||                         |    |  781250|    |                   
2*W\-log\5       // + log(30517578125)   2*W\-log\5       /, -1/ + log(30517578125)
-------------------------------------- + ------------------------------------------
               6*log(5)                                   6*log(5)

\frac{2 W_{-1}\left(- \log{\left(5^{\frac{3 \sqrt{5}}{781250}} \right)}\right) + \log{\left(30517578125 \right)}}{6 \log{\left(5 \right)}} + \frac{2 W\left(- \log{\left(5^{\frac{3 \sqrt{5}}{781250}} \right)}\right) + \log{\left(30517578125 \right)}}{6 \log{\left(5 \right)}}

   /    /     ___\\                         /    /     ___\    \                   
   |    | 3*\/ 5 ||                         |    | 3*\/ 5 |    |                   
   |    | -------||                         |    | -------|    |                   
   |    |  781250||                         |    |  781250|    |                   
2*W\-log\5       // + log(30517578125)   2*W\-log\5       /, -1/ + log(30517578125)
-------------------------------------- + ------------------------------------------
               6*log(5)                                   6*log(5)

\frac{2 W_{-1}\left(- \log{\left(5^{\frac{3 \sqrt{5}}{781250}} \right)}\right) + \log{\left(30517578125 \right)}}{6 \log{\left(5 \right)}} + \frac{2 W\left(- \log{\left(5^{\frac{3 \sqrt{5}}{781250}} \right)}\right) + \log{\left(30517578125 \right)}}{6 \log{\left(5 \right)}}

product

   /    /     ___\\                       /    /     ___\    \                   
   |    | 3*\/ 5 ||                       |    | 3*\/ 5 |    |                   
   |    | -------||                       |    | -------|    |                   
   |    |  781250||                       |    |  781250|    |                   
2*W\-log\5       // + log(30517578125) 2*W\-log\5       /, -1/ + log(30517578125)
--------------------------------------*------------------------------------------
               6*log(5)                                 6*log(5)

\frac{2 W\left(- \log{\left(5^{\frac{3 \sqrt{5}}{781250}} \right)}\right) + \log{\left(30517578125 \right)}}{6 \log{\left(5 \right)}} \frac{2 W_{-1}\left(- \log{\left(5^{\frac{3 \sqrt{5}}{781250}} \right)}\right) + \log{\left(30517578125 \right)}}{6 \log{\left(5 \right)}}

/   /    /     ___\\                   \ /   /    /     ___\    \                   \
|   |    | 3*\/ 5 ||                   | |   |    | 3*\/ 5 |    |                   |
|   |    | -------||                   | |   |    | -------|    |                   |
|   |    |  781250||                   | |   |    |  781250|    |                   |
\2*W\-log\5       // + log(30517578125)/*\2*W\-log\5       /, -1/ + log(30517578125)/
-------------------------------------------------------------------------------------
                                            2                                        
                                      36*log (5)

\frac{\left(2 W\left(- \log{\left(5^{\frac{3 \sqrt{5}}{781250}} \right)}\right) + \log{\left(30517578125 \right)}\right) \left(2 W_{-1}\left(- \log{\left(5^{\frac{3 \sqrt{5}}{781250}} \right)}\right) + \log{\left(30517578125 \right)}\right)}{36 \log{\left(5 \right)}^{2}}

(2*LambertW(-log(5^(3*sqrt(5)/781250))) + log(30517578125))*(2*LambertW(-log(5^(3*sqrt(5)/781250)), -1) + log(30517578125))/(36*log(5)^2)

Numerical answer [src]

x1 = 2.49999713779343

x2 = -0.361289616528727

x2 = -0.361289616528727

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0,008^x=5^1-2x equation

Numerical solution:

The solution