How to expand, then evaluate, and simplify this log question:
logbase7 (49( 3sqrt x^5))
I put the brackets in myself, I there were originally no brackets nor spaces in the question
I think your putting in brackets changed the meaning of the function.
To expand, evaluate, and simplify the given logarithmic expression, we need to follow a step-by-step process.
Step 1: Expand the expression inside the logarithm:
Start by applying the power rule of logarithms, which states that log(base b) (ab) = log(base b) (a) + log(base b) (b):
log(base 7) (49(3√x^5)) = log(base 7) (49) + log(base 7) (3√x^5)
Since 49 is a perfect square, we can simplify it further:
log(base 7) (49) = 2
Substituting this back into the previous expression, we have:
log(base 7) (49(3√x^5)) = 2 + log(base 7) (3√x^5)
Step 2: Evaluate the expression inside the logarithm:
To evaluate the expression √x^5, we need to simplify the square root. Remember that the square root can be expressed as a fractional exponent:
√(x^5) = (x^5)^(1/2) = x^(5/2)
Substituting this back into the previous expression, we have:
2 + log(base 7) (3x^(5/2))
Step 3: Simplify the expression further:
Finally, we simplify the expression by combining the logarithmic term:
log(base 7) (3x^(5/2)) is already in its simplest form.
Hence, the expanded, evaluated, and simplified form of the given logarithmic expression is:
2 + log(base 7) (3x^(5/2))