Question

If log subscript b 5 equals z then the value of log subscript b squared end subscript 5 is given by z over 2 z squared z None of the above

Answer 1

Given:

$log_b 5 =z$

To find:

$log_{b^2} 5 =?$

First of all, let us have a look at some basic formula of Log:

$1.\ log_pq=\dfrac{log_rq}{log_p}$  (A new base of log 'r' in numerator and denominator both)

$2.\ log_rp^q= q\times log_rp$ (Power inside i.e. q comes outside of log in multiplication with log.)

$3.\ log_pp = \dfrac{log_rp}{log_rp} = 1$

We will use above formula to solve $log_{b^2} 5.$

$log_{b^2} 5 = \dfrac{log_b5}{log_bb^2}$ (Using formula 1, base 'r' = b, q = 5 and p = $b^2$)

Now using Formula 2 in the denominator:

$\dfrac{log_b5}{2\times log_bb}$

Now, using Formula 3 to solve $log_bb$ in the denominator, putting $log_bb$ = 1

$\dfrac{log_b5}{2}\\\Rightarrow \dfrac{1}{2} \times log_b5$

Now, it is given that $log_b5 =z$

So the answer is:

$log_{b^2} 5 =\dfrac{z}{2}$

So, the answer is "z over 2" or $\frac{z}{2}$.