Answer:
Step-by-step explanation:
For #6, first use the rule to "undo" the division. That rule is subtraction:
[tex]log(x^2y^6-z^3)[/tex]
Now "undo" the multiplication with addition:
[tex]log(x^2+y^6-z^3)[/tex]
The last rule is to pull down the exponent to the front:
[tex]log(2x+6y-3z)[/tex]
For #7, begin by setting each expression equal to x, what we are solving for.
[tex]log_{4}18=x[/tex]
Writing this as an exponent:
[tex]4^x=18[/tex]
Take the natural log of both sides:
[tex]ln(4^x)=ln(18)[/tex]
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.
[tex]log_{\frac{1}{2} }74=x[/tex] and
[tex]\frac{1}{2}^x=74[/tex] and
[tex]ln(\frac{1}{2})^x=ln(74)[/tex] and
[tex]xln(\frac{1}{2})=ln(74)[/tex] and divide both sides by ln(1/2) to get that
x = -6.21
