Question

If x = 1 + ${\log }_a$ bc. Find the value of ${\log }_{abc}$ a in terms of x.

• A. x
• B.
• C.
• D. 2x

Answer 1

The correct option is B

Given x = 1 + ${\log }_a$bc

x - 1 = ${\log }_a$bc -----------------(1)

Here we see, ${\log }_a$bc in base a, we need to find the value of ${\log }_a$bc a.

bc can be written as $\frac{abc}{a}$

From equation 1

x - 1 = ${\log }_a$ $\frac{abc}{a}$ = ${\log }_a$abc - ${\log }_a$a

x - 1 = ${\log }_a$ abc - 1

${\log }_a$ abc = x

We know, ${\log }_{a}x$ = $\frac{1}{{\log }_{x}a}$

${\log }_{a}abc$ = x

${\log }_{abc}a$ = $\frac{1}{{\log }_{a}abc}$ = $\frac{1}{x}$

${\log }_{abc}a$ = $\frac{1}{x}$