a. Find the possible value for x in the equation 3x = 7 (mod 2) b. Simplify: log3 27 + log3 9 c. If log5 x = 3 and log5 y = 2, find the value of log5 (x / y)

Here's how to simplify the expression: Step 1: Recognize that 27 and 9 can be expressed as powers of 3. 27 = 3³; 9 = 3² Step 2: Substitute these values into the logarithmic expression. log₃ 27 + log₃ 9 = log₃ (3³) + log₃ (3²); Step 3: Apply the logarithm property log_b (b^k) = k. log₃ (3³) + log₃ (3²) = 3 + 2 Step 4: Perform the addition. 3 + 2 = 5 The simplified expression is: 5

a. Find the possible value for x in the equation 3x = 7 (mod 2) b. Simplify: log3 27 + log3 9 c. If log5 x = 3 and log5 y = 2, find the value of log5 (x / y)

Here's how to simplify the expression: Step 1: Recognize that 27 and 9 can be expressed as powers of 3. 27 = 3³; 9 = 3² Step 2: Substitute these values into the logarithmic expression. log₃ 27 + log₃ 9 = log₃ (3³) + log₃ (3²); Step 3: Apply the logarithm property log_b (b^k) = k. log₃ (3³) + log₃ (3²) = 3 + 2 Step 4: Perform the addition. 3 + 2 = 5 The simplified expression is: 5

Solved: A. Find the possible value for x in the equation 3x…

Here's how to simplify the expression:

Recognize that 27 and 9 can be expressed as powers of 3.
$27 = 3^3$ $9 = 3^2$
Substitute these values into the logarithmic expression.
$\log_3 27 + \log_3 9 = \log_3 (3^3) + \log_3 (3^2)$
Apply the logarithm property $\log_b (b^k) = k$ .
$\log_3 (3^3) + \log_3 (3^2) = 3 + 2$
Perform the addition.
$3 + 2 = 5$
The simplified expression is:
$\boxed{\text{5}}$

A. Find the possible value for x in the equation 3x = 7 (mod 2) b. Simplify: log3 27 + log3 9 c. If log5 x = 3 and log5 y = 2, find the value of log5 (x / y)

Step-by-step solution

Recognize that 27 and 9 can be expressed as powers of 3.

Substitute these values into the logarithmic expression.

Apply the logarithm property $\log_b (b^k) = k$ .

Perform the addition.

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