Question

If 3/2 log a + 2/3 log b - 1 = 0, find the value of a9*b4

Answer 1

3/2loga + 2/3logb -1 = 0

9loga + 4logb - 6 = 0

use concept ,
nlogm = logm^n
and logm + logn = logmn

loga^9 + logb^4 = 6
log(a^9.b^4) = 6
a^9.b^4 = 10^6

hence, a^9.b^4 = 10^6

Answer 2

3/2loga + 2/3log b - 1 = 0

Multiplying by 6

6(3/2) log a +6 ( 2/3)-6 = 0

9 log a + 4 log b - 6 = 0

9 log a + 4 log b = 6

$log {a}^{9} + log {b}^{4} = 6$

$log( {a}^{9} \times {b}^{4} )$ = 6

$10^{6} = {a}^{9} \times {b}^{4}$