The expression into a single logarithm is ![log[(x)^{10}][(2)^{30}]](https://tex.z-dn.net/?f=log%5B%28x%29%5E%7B10%7D%5D%5B%282%29%5E%7B30%7D%5D)
Step-by-step explanation:
Let us revise some logarithmic rules
∵ 10 log(x) + 5 log(64)
- At first re-write 10 log(x)
∴ 10 log(x) = 
- Then re-write 5 log(64)
∴ 5 log(64) = 
∴ 10 log(x) + 5 log(64) =
+ 
- Use the 3rd rule above to make it single logarithm
∵
+
= ![log[(x)^{10}][(64)^{5}]](https://tex.z-dn.net/?f=log%5B%28x%29%5E%7B10%7D%5D%5B%2864%29%5E%7B5%7D%5D)
∴ 10 log(x) + 5 log(64) = ![log[(x)^{10}][(64)^{5}]](https://tex.z-dn.net/?f=log%5B%28x%29%5E%7B10%7D%5D%5B%2864%29%5E%7B5%7D%5D)
∵ 64 = 2 × 2 × 2 × 2 × 2 × 2
∴ We can write 64 as 
∴ 
- Multiply the two powers of 2
∴ 
∴ 10 log(x) + 5 log(64) = ![log[(x)^{10}][(2)^{30}]](https://tex.z-dn.net/?f=log%5B%28x%29%5E%7B10%7D%5D%5B%282%29%5E%7B30%7D%5D)
The expression into a single logarithm is ![log[(x)^{10}][(2)^{30}]](https://tex.z-dn.net/?f=log%5B%28x%29%5E%7B10%7D%5D%5B%282%29%5E%7B30%7D%5D)
Learn more:
You can learn more about the logarithmic functions in brainly.com/question/11921476
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