Please express in terms of sums and differences in logarithms.
log a x^3 y^2 z
Add the logs of every term in the product. For the x^3 term, you get 3logx. You do the rest. Let us know if you want your answer checked
1 log a 3log x 2log y 1 logz Is this correct?
No. You have to add the logs of each term. Remember that
log (abc) = log a + log b + log c etc.
Your answer should be
log (a x^3 y^2 z) = log a + 3 log x + 2 log y + log z
Please express in terms of sums and differences in logarithms.
log a x^3 y^2 z
For log_a (x^3) we can use the rule
log_b (m^n) = nlog_b (x).
The log_a (x^3) becomes 3xlog_a (x).
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We usethe same rule for y^2.
y^2 becomes 2log_y.
And finally, z becomes log_z.
We now use the sum rule:
log_b(mn) = log_b(m) + log_b(n).
3log_a(x) + 2log_y + log_z
To express log a (x^3 y^2 z) in terms of sums and differences in logarithms, we can use the properties of logarithms.
First, let's break down the expression into the product of its individual terms: x^3 y^2 z.
Then, we can rewrite the expression as a sum of logarithms of each individual term:
log a (x^3 y^2 z) = log a (x^3) + log a (y^2) + log a (z)
Next, we can further simplify each term using the power rule of logarithms:
log a (x^3) = 3 log a (x)
log a (y^2) = 2 log a (y)
So, the expression can be further simplified as:
log a (x^3 y^2 z) = 3 log a (x) + 2 log a (y) + log a (z)
Therefore, in terms of sums and differences in logarithms, the expression log a (x^3 y^2 z) can be expressed as 3 log a (x) + 2 log a (y) + log a (z).