Verified answer

for the first part, you have to make the assumption that x and y are real numbers otherwise there is no unique solution. That is, if they are not both real valued, then chose any y and let

x = (1 /3) * ( ( 7 y - 4) i - 5)

If they are both real valued then, since the real parts must be equal and the imaginary parts must be equal,

4 = 7 y

and

-3 x = 5

or

y = 4 / 7

x = - 5 / 3

For the second part, if you remember the part about the sum and difference of log functions, i.e.

log (x * y) = log(x) + log (y)

and

log (x / y) = log(x) - log(y)

it makes the problem easier. I will assume log is log base 10 so that log(10^5) = 5 and the first of the equations becomes

y = log(x) + log(10^5) = log(10^5 * x)

Thus

x + 5 = 10^5 x

or

x = 5 / (10^5 - 1) ~ .0000500005

so that

y ~ 0.69897435

Another way which doesn't depend on remembering the sum and difference log rules is to rewrite the equations by raising quantities to a poser of 10 and remembering that

10^(log(a)) = a

Write the first equation as

y - 5 = log(x)

and raise both sides to that power of ten:

10^(y-5) = 10^y / 10^5 = x

or 10^y = 10^5 x

Now the other equation to a power of ten gives

10^y = x + 5

which leads to the same equation for x as above.

4-3x(i) = 7y + 5(i)

7y = -3x(i) - 5(i) + 4

49Y = -9x'2 - 21

Y = -9/49x'2- 3/7

Now do a quadratic to solve for x. Im too tired to haha

Idk the other