Consider the relationship f(x)=2^x and g(x)=log2 x.the equations 2^x and log_(2)(8) = x \: has \: the \: same \: solutionTrueor False

Question

Consider the relationship f(x)=2^x and g(x)=log2 x.the equations 2^x and
`log_(2)(8) = x \: has \: the \: same \: solution`Trueor False

Answer 1

`f(x)=2^x`
`g(x)=\log _2x`

To find the solution of the equations:

1. Knowing the next property of logarithms:

`\log _ax=y\Rightarrow a^y=x`

The equation:

`\log _28=x`

Is equal to:

`2^x=8`You can see that the equations are differents, as the first one is 2^x (2^x=0) and the second one is 2^x=8. Then, the solutions are differents.