solve the following equations for y

Question

log2(15 y+12) = 8x7+7

2e2 y−4 = x5−3

Answer 1

Greetings! Lets solve these two shall we!?

log₂(15 y+12) = 8x⁷+7..............First we raise both sides as exponents with base 2 as

2^log2(15y+12) = 2^8x7+7......................... 2^log2 is equal to 1 so

15y + 12 = 2^8x7+7..........................Now we subtract 12 to both sides

15y = 2^8x7+7 - 12.............................Then finally divide 15 to get

y = (2^8x7+7 - 12) / 15

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Now its time to solve the other problem!

2e^2 y−4 = x⁵−3................................First we divide the 2 to both sides to obtain

e^2y-4 = (x⁵-3) / 2...............................Then we take the natural log of both sides to get

(2y-4)lne = ln [(x⁵-3) / 2].........................Note that ln(e) equals 1. So

2y - 4 = ln [(x⁵-3) / 2].....................Now we add 4

2y = ln [(x⁵-3) / 2] + 4...................Finally we divide 2 to get the solution

y = [ln [(x⁵-3) / 2] + 4] / 2

I hope this helped!