Answer:
x = 2.3202
Step-by-step explanation:
Given equation:
on taking log both sides, we get
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
Let's say that the value invested in the account with a rate of 8% is "x", then the amount invested in the account with a rate of 12% is:
To calculate the total interest we need to calculate the interest of each individual account and sum them:
The total interest is the sum of the two expressions above:
The value invested in the account with 8% interest is 830, the one invested in the account with 12% interest is 1280.