Question

Solve for \( x \): \( \log(x) + \log(5) = \log(20) \).

Hint:

When logs with the same base are equal, you can equate their arguments directly after combining terms using log rules.

Answer 1

Given Equation:
log(x) + log(5) = log(20)

Step 1: Use the Logarithmic Identity
We know that:
log a + log b = log (ab)

Applying this identity:
log(x × 5) = log(20)

So,
log(5x) = log(20)

Step 2: Equate the Arguments
If log A = log B, then A = B (for positive values).

Therefore,
5x = 20

Step 3: Solve for x
x = 20 / 5
x = 4

Final Answer:
x = 4