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Genrish500 [490]
2 years ago
5

3

Mathematics
1 answer:
Marianna [84]2 years ago
6 0

The expression into a single logarithm is log[(x)^{10}][(2)^{30}]

Step-by-step explanation:

Let us revise some logarithmic rules

  • log(a)^{n}=nlog(a)
  • log(ab)=log(a)+log(b)
  • nlog(a)+mlog(b)=log[(a)^{n}][(b)^{m}]

∵ 10 log(x) + 5 log(64)

- At first re-write 10 log(x)

∴  10 log(x) = log(x)^{10}

- Then re-write 5 log(64)

∴  5 log(64) = log(64)^{5}

∴ 10 log(x) + 5 log(64) = log(x)^{10} + log(64)^{5}

- Use the 3rd rule above to make it single logarithm

∵ log(x)^{10} + log(64)^{5} = log[(x)^{10}][(64)^{5}]

∴ 10 log(x) + 5 log(64) = log[(x)^{10}][(64)^{5}]

∵ 64 = 2 × 2 × 2 × 2 × 2 × 2

∴ We can write 64 as 2^{6}

∴ (64)^{5}=(2^{6})^{5}

- Multiply the two powers of 2

∴ (64)^{5}=(2)^{30}

∴ 10 log(x) + 5 log(64) = log[(x)^{10}][(2)^{30}]

The expression into a single logarithm is log[(x)^{10}][(2)^{30}]

Learn more:

You can learn more about the logarithmic functions in brainly.com/question/11921476

#LearnwithBrainly

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