Question

Show that $\log_{6}7 = \frac{\log_{7}}{1+\log_{2}3}$.

Answer 1

Answer:

Step-by-step explanation:

Hi,

Consider L.H.S = log₆7

Using change of base property , changing base of logarithm

to 2, we can write as

= log ₂7/log₂ 6

But 6 = 2*3

So, log ₂6 = log₂ (2*3)

Using Addition Property of logarithm

log x + log y = log (xy)

We can write log ₂6 = log₂ 2 + log ₂3

But log ₂2 = 1 , So

log ₂6 = 1 + log₂3

Hence, L.H.S

= log₂7/(1 + log₂3)

= R.H.S

Hope, it helps !