Explain the process to solving for all possible integer values of a and b with the equation log3 (a) + log3 (b) = 4, without solving it!

  write factor pairs of 3^4

Step-by-step explanation:

Take the anti-log, then identify integer factor pairs of the number on the right side of the equal sign. One of the factors in each pair is the value of "a", the other is the value of "b".

The solution you didn't want to see

Take the antilog:

  ab = 3^4

Find factor pairs of 3^4:

  3^4 = 1×81 = 3×27 = 9×9 = 27×3 = 81×1

Possible solutions are ...

  (a, b) ∈ {(1, 81), (3, 27), (9, 9), (27, 3), (81, 1)}

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°