Question

Use properties of logarithms to solve the logarithmic equation. Round to 4 decimal places where needed. (If an answer does not exist, enter DNE.)
log2(3 + 8x) − log2(2x − 1) = 3

Answer 1

Use Log property:
 log a - log b = log (a/b)

$log_2 \frac{3+8x}{2x-1} = 3$
Next use Property:
$(log_b x = y) ==\ \textgreater \ (x = b^y)$
...
$\frac{3+8x}{2x-1} = 2^3 = 8$
3+8x = 8(2x-1) = 16x-8
8x = 11

$x = \frac{11}{8}$