Question

Determine the value of the following
Log 1 to the base 7

Answer 1

Answer:

$log_{7}(1) = 0 \\ \\ because \: log \: 1 \: to \: the \: base \: \\ anything \: is \: 0$

Hope it helps ✌,✌

# follow me

Answer 2

Answer :-

$\tt \: log_{7}1 = 0$

Solution :-

Let $\tt log_{7}1 = x$

Write it in exponential form

$\tt {7}^{x} = 1$

$\boxed{ \sf If \: log_{a}N = x \: then \: {a}^{x} = N}$

Now make the bases equal

$\tt 7^x = 7^0$

[ Law af exponents used $\bf a^0 = 1$ Here a = 7]

If bases are equal exponents must be equal

$\tt x = 0$

$\tt \implies log_{7}1 = 0$

$\tt \therefore \: log_{7}1 = 0$

Laws of exponents used :-

$\sf \rightarrow \: a^{0} = 1$

$\sf \rightarrow a^m = a^n \: then \: m = n$

Extra Information :-

$\rightarrow$ Exponential form and logarithm form are inverve to each other.

$\rightarrow$ In general a and N are positive real number such that a ≠ 1 we define $\tt log_{a}N = x \implies a^x = N.$