Using some logarithmic properties, we will see that the solution of the logarithmic equation is 10.5
How to find the value of the logarithm?
Here we have some properties that you need to remember.
log(A*B) = log(A) + log(B)
log(A/B) = log(A) - log(B)
log(Aⁿ) = n*log(A)
Then we can rewrite our equation as:
[log(x²) + log(√z)] - log(y³)
Now, remember that a square root is equal to an exponent of 0.5, then:
[log(x²) + log(√z)] - log(y³) = 2*log(x) + 0.5*log(z) - 3*log(y)
Now we can replace the logarithms by the given values:
2*log(x) + 0.5*log(z) - 3*log(y)
2*7 + 0.5*5 - 3*2 = 10.5
The solution of the logarithmic equation is 10.5
If you want to learn more about logarithms:
https://brainly.com/question/13473114
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