Respuesta :

THEBRAINLY1

[tex]b {}^{x} = n \\ taking \: log \: on \: both \: the \: sides \: \\ log(b {}^{x} ) = log(n) \\ x( log(b) ) = log(n) \\ x = \frac{ log(n) }{ log(b) } \\ x = log_{b}(n) [/tex]

Answer:  The required logarithmic form of the given equation is [tex]x=\log_bN.[/tex]

Step-by-step explanation:  We are given to express the following equation in logarithmic form :

[tex]b^x=N~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We know that

The logarithmic form of an exponential equation [tex]a^C=b[/tex] is given by

[tex]C=\log_ab.[/tex]

So, from equation (i), we get

[tex]b^x=N\\\\\Rightarrow x=\log_bN.[/tex]

Thus, the required logarithmic form of the given equation is [tex]x=\log_bN.[/tex]

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