Question

I need help!!

Use the properties of logarithms to simplify.

log base5 5^(2x − 9) + log base3 729^5

Answer 1

1/2log base 3 of x + log base 3 of x =6

As the multiplication law of logarithms states that when it's addition you multiply and vice versa:log base c of xy=log base c of x + log base c of y

log base 3 of ( x1/2×x)=6

36=729

x1/2×x=729 since it's multiplication you add the powers so 1/2 +1 =3/2

x3/2=729

So square 729. 7292=531441. Now take a cube root. Cube root of 531441 is 81

X=81