Rewrite the following as an equivalent logarithmic
equation.Do not solve.
y^t = x
answer logy+logt=logx-is this right
also
Express as an equivalent expression that is a sum of logt (3ab) the t is at the bottom of the g
answer log3+loga+logb
logarithms.
t log y = log x
is an equivalent equation.
In your second question, it seems that t is the base of the logarithm, so
logt(3ab) = logt(3) + logt(a) + logt(b)
To rewrite the equation y^t = x as an equivalent logarithmic equation, we need to isolate the logarithm. To do this, we take the logarithm of both sides of the equation. However, we must specify the base of the logarithm for clarity.
Assuming we want to rewrite the equation using a logarithm with base y, we take the logarithm base y of both sides:
logy(y^t) = logy(x)
Using the logarithm property logb(b^a) = a, we can simplify the left side:
t = logy(x)
Now we have the equation in logarithmic form: t = logy(x).
Regarding your first answer, logy + logt = logx, it is not correct. When you have an equation with powers on one side (y^t) and a variable on the other side (x), taking the logarithm of both sides results in a logarithmic equation where the base of the logarithm is the base used in the original equation.
For the second part of the question, expressing 3ab as an equivalent expression that is a sum of logarithms, we break it down using the logarithmic properties:
logt(3ab) = logt(3) + logt(a) + logt(b)
Therefore, the expression logt(3ab) is equivalent to logt(3) + logt(a) + logt(b), which represents a sum of logarithms.