# If log 18 to the base 12=a and log 54 to the base 24=b,prove that ab+5(a-b)=1?

##### 2 Answers

Jul 11, 2017

see explanation

#### Explanation:

Please check to make sure I've read the problem correctly. Logarithms may be written wrong...

#\log_12(18)=a# #\log_24(54)=b#

Jul 12, 2017

Please see below.

#### Explanation:

As

i.e.

or

similarly as

i.e.

or

Comparing the two **........(A)**

and **........(B)**

Subtracting **(A)** from **(B)**, we get

and

hence

(Note that **(B)** gives