Question

Please help me with the following questions. Thanks in advance!

Answer 1

Answer:

Step-by-step explanation:

For #6, first use the rule to "undo" the division.  That rule is subtraction:

$log(x^2y^6-z^3)$

Now "undo" the multiplication with addition:

$log(x^2+y^6-z^3)$

The last rule is to pull down the exponent to the front:

$log(2x+6y-3z)$

For #7, begin by setting each expression equal to x, what we are solving for.

$log_{4}18=x$

Writing this as an exponent:

$4^x=18$

Take the natural log of both sides:

$ln(4^x)=ln(18)$

Following the same rule as above, we can pull the x down front:

x ln(4)= ln(18)

To solve for x, just divide both sides by ln(4) to get that

x = 2.08

Do the same thing for 7b.

$log_{\frac{1}{2} }74=x$ and

$\frac{1}{2}^x=74$ and

$ln(\frac{1}{2})^x=ln(74)$ and

$xln(\frac{1}{2})=ln(74)$ and divide both sides by ln(1/2) to get that

x = -6.21