Question

1) write the expression as a single logarithm log3 40 - log3 10 show work. 2) solve the exponential equation 1/16 =64^[4x-3]

Answer 1

1) The expression log3(40) - log3(10) can be simplified. When substracting logs with the same base values, in this case 3, you can simplify the expression by dividing the species inside each log.

log3(40) - log3(10)
log3(40/10)
log3(4) = simplified expression

2) To solve the exponential equation 1/16 = 64^(4x-3) we can also simplify things first. 16 = 4², and 64 = 4³.

1/4² = 4³⁽⁴ˣ⁻³⁾
4⁻² = 4³⁽⁴ˣ⁻³⁾

At this stage since the bases are equal, the exponents must also be equal.

-2 = 3(4x-3)
-2/3 = 4x - 3
4x = 7/3
x = 7/12