Write as a single logarithm. Thank-you.
3(4 log t^2)
Would it be logt^8 or are you not allowed to do that?
And
logy-4(logr+2logt)
in the first one, what happened to the 3?
my answer is log t^24
in the second...
=logy - 4(logr + logt^2)
=logy - 4log rt^2
= logy - log r^4t^8
=log(y/(r2t8))
correction, last line
log(y/(r4t8))
For the expression 3(4 log t^2), you can use the power rule of logarithms to rewrite it as a single logarithm.
First, apply the power rule:
3(4 log t^2) = 12 log t^2
Next, you can use the property of logarithms stating that the coefficient in front of the logarithm can be moved as an exponent inside the logarithm:
12 log t^2 = log (t^2)^12
Lastly, simplify the exponent:
log (t^2)^12 = log t^24
So the single logarithm equivalent of 3(4 log t^2) is log t^24.
For the expression logy - 4(logr + 2logt), let's simplify it step-by-step.
First, use the property of addition inside the logarithm and the power rule of logarithms:
log(y) - 4(logr + 2logt) = log(y) - 4(logr) - 4(2logt)
Next, apply the power rule:
log(y) - 4(logr) - 4(2logt) = log(y) - log(r^4) - log(t^8)
Now, use the property of subtraction inside the logarithm:
log(y) - log(r^4) - log(t^8) = log(y/(r^4 * t^8))
Therefore, the single logarithm equivalent of logy - 4(logr + 2logt) is log(y/(r^4 * t^8)).