Name: Logarithm properties: solution walkthrough
Uploaded: 2026-11-13
Duration: 1 min 46 s
Description: What is the value of log_4 2 + log_4 32? Try it, then watch the animated solution.

Logs with the same base add by multiplying inside:

\log_b M + \log_b N = \log_b (MN)

.

Both logs have base

4

, so

\log_4 2 + \log_4 32 = \log_4 (2 \cdot 32) = \log_4 64

.

Ask:

4

to what power is

64

?

4 \cdot 4 \cdot 4 = 64

, so

4^3 = 64

and

\log_4 64 = 3

.

On a scale in powers of

4

, the two logs are lengths

\tfrac{1}{2}

and

\tfrac{5}{2}

. Together they reach

3

.

Traps:

64

forgets the log,

6

uses base

2

, and

\log_4 34

adds the numbers inside.

Try it first