Question

Please send the solution of this sum. I will mark you brainliest ​

Answer 1

Answer:

The second term above, with just a "5" inside, is as "expanded" as it can get, because there's only just the one thing inside the log. And, because 5 is not a power of 2, there's no simplification I can do. So that part of the expansion is done; I'll just be carrying the "log(5)" along for the ride to the final answer.

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In the first term, though, there's still more than just one thing inside the log. In particular, I see that there's an exponent inside the log. However, I can't take the exponent out front yet, because that power is only on the x, not the 8. I have to remember that the rule says that I can only take the exponent out front if it is "on" everything inside the log. So I first need to isolate that part of the argument that has the power on it.

The 8 is multiplied onto the x4, so I can split the factors inside the log by converting to added logs:

log2(8x4) – log2(5) = log2(8) + log2(x4) – log2(5)

Since 8 is a power of 2 (namely, 23), I can simplify the first log to an exact value. Because 23 = 8, then log2(8) = 3, so I get:

log2(8) + log2(x4) – log2(5)

= 3 + log2(x4) – log2(5)

Okay; now I'm finished with the first term, too; I'm only left with the middle term to expand, with the exponent inside its log.

The variable x has the exponent (which is now "on" everything inside its log), so I can use a log rule and move the exponent out in front of the log as a multiplier:

log2(8) + log2(x4) – log2(5)

= 3 + 4log2(x) – log2(5)

Each log now finally contains only one thing, and the first log term has been simplified to a numerical value, so this expression is fully expanded. Then my final answer is:

3 + 4log2(x) – log2(5)