Answer:
x = 2.3202
Step-by-step explanation:
Given equation:
[tex]10^{(3x-5)} = 7^x[/tex]
on taking log both sides, we get
[tex]\log(10^{(3x-5))} =\log(7^x)[/tex]
now,
using the property of log function
log(aᵇ) = b × log(a)
therefore,
we get
(3x-5)log(10) = xlog(7)
now,
log(10) = 1
and
log(7) = 0.84509
thus,
( 3x - 5 ) × 1 = 0.84509x
or
3x - 0.84509x - 5 = 0
or
2.15491x = 5
or
x = 2.3202
