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6^x+5=36

6^x+5=36 equation

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Numerical solution:

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The solution

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 x         
6  + 5 = 36
$$6^{x} + 5 = 36$$
Detail solution
Given the equation:
$$6^{x} + 5 = 36$$
or
$$\left(6^{x} + 5\right) - 36 = 0$$
or
$$6^{x} = 31$$
or
$$6^{x} = 31$$
- this is the simplest exponential equation
Do replacement
$$v = 6^{x}$$
we get
$$v - 31 = 0$$
or
$$v - 31 = 0$$
Move free summands (without v)
from left part to right part, we given:
$$v = 31$$
We get the answer: v = 31
do backward replacement
$$6^{x} = v$$
or
$$x = \frac{\log{\left(v \right)}}{\log{\left(6 \right)}}$$
The final answer
$$x_{1} = \frac{\log{\left(31 \right)}}{\log{\left(6 \right)}} = \frac{\log{\left(31 \right)}}{\log{\left(6 \right)}}$$
The graph
Sum and product of roots [src]
sum
log(31)
-------
 log(6)
$$\frac{\log{\left(31 \right)}}{\log{\left(6 \right)}}$$
=
log(31)
-------
 log(6)
$$\frac{\log{\left(31 \right)}}{\log{\left(6 \right)}}$$
product
log(31)
-------
 log(6)
$$\frac{\log{\left(31 \right)}}{\log{\left(6 \right)}}$$
=
log(31)
-------
 log(6)
$$\frac{\log{\left(31 \right)}}{\log{\left(6 \right)}}$$
log(31)/log(6)
Rapid solution [src]
     log(31)
x1 = -------
      log(6)
$$x_{1} = \frac{\log{\left(31 \right)}}{\log{\left(6 \right)}}$$
x1 = log(31)/log(6)
Numerical answer [src]
x1 = 1.91654475026417
x1 = 1.91654475026417
The graph
6^x+5=36 equation