`2^(3-z) = 625` Solve the equation accurate to three decimal places

For exponential equation:`2^(3-z)=625` , we may apply the logarithm property:

`log(x^y) = y * log (x)` .

This helps to bring down the exponent value.

 Taking "log" on both sides:

`log(2^(3-z))=log(625)`

`(3-z)* log (2) = log(625)`

Divide both sides by log (2) to isolate (3-z):

`((3-z) * log (2)) /(log(2))= (log(625))/(log(2))`

`3-z=(log(625))/(log(2))`

Subtract both sides by 3 to isolate "-z":

`3-z=(log(625))/(log(2))`

-3                            -3

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`-z=(log(625))/(log(2)) -3`

Multiply both sides by -1 to solve +z or z:

`(-1)*(-z)=(-1)* [(log(625))/(log(2)) -3]`

` `

 `z~~-6.288 `       Rounded off to three decimal places.

To check, plug-in `z=-6.288` in `2^(3-z)=625` :

`2^(3-(-6.288))=?625`

`2^(3+6.288)=?625`

`2^(9.288)=?625`

`625.1246145~~625`   TRUE

Conclusion: `z~~-6.288` as the final answer.