A level Maths questions help

Solve the following simultaneous logarithmic equations
y^logx=100
log(sqrt(xy/10))=1
given further that x , y ∈ℝ , with x > 0 , y > 0.
Can someone help me with this question, I keep getting an unsolvable quadratic.

upload what you tried?
Im presuming log is tne natural log, but to get a handle on (guess) the solution, you could assume it was base 10

I realised i made a simple mistake and figured it out, but thanks for the help. Though i am confused on the next one, could i upload that instead?

sure

And what do you understand / have problem with?

im not really sure where to start

im not really sure where to start

The first line says the rate of change of the gradient is constant.
So write that down clearly and try and solve for that.

ive got a few simultaneous equations:
m+c=-1/2
2=m/2+c+d
9m-3c-d=0
Do i solve for m,c, and d, then equate the final function to y=2x to work out where they intersect and then use definite integration to find out area under the curve and subtract it from the area under the line?

What curve did you get from the first part (what are the parameters m,c,d)?

Assuming its a quadratic etc, then yes you need to find the points of intersection (roots of curve-line) then use integration to find the area between the curve and the line. So integrate curve-line between the two roots.

Sorry i had to redo my workings because i made some mistakes but hopefully it is right this time. I got:
m=-1 c=0.5 d=1.5
But yes it is a quadratic.

Ive not done the numbers, but a quadratic is easy to verify for the 3 points.
So just integrate the curve-line between the roots.

What is the easiest way to tackle this question?

Any ideas?

Solve the following simultaneous logarithmic equations
y^logx=100
log(sqrt(xy/10))=1
given further that x , y ∈ℝ , with x > 0 , y > 0.
Can someone help me with this question, I keep getting an unsolvable quadratic.

I see, i'll start by factorising the quadratic

upload what you tried?
Im presuming log is tne natural log, but to get a handle on (guess) the solution, you could assume it was base 10.