Question

log15(x^2+13)=log15(-9x-1)

Answer 1

\[log_{_{15}}(x^2+13)=log_{_{15}}(-9x-1)\]we have 2 logarithms with the same basis, then we can cancel the logs\[x^2+13=-9x-1\]\[x^2+13+9x+1=0\]\[x^2+9x+14=0\]\[\boxed{\boxed{x_1=-2~~and~~x_2=-7}}\]

Answer 2

log19(X ^{2}+17)=log19(8x+2)

Answer 3

The same way:\[log_{_{19}}(x^2+17)=log_{_{19}}(8x+2)\]the same basis, then we can cancel the logs\[x^2+17=8x+2\]\[x^2+17-8x-2=0\]\[x^2-8x+16=0\]\[\boxed{\boxed{x_1=x_2=4}}\]