SOLUTION: Express as a single logarithm, and, if possible, simplify?? 4 loga y + 1/7 loga z Thank you for your help!

Question 250423: Express as a single logarithm, and, if possible, simplify??
4 loga y + 1/7 loga z
Thank you for your help!
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the rules of logarithms state:

(rule 1)

(rule 2)

(rule 3)

your expression is:

by rule 3.

by rule 3.

your expression becomes:

this becomes by rule 1.

since can also be written as , this can also be written as:

you can prove that your original expression of is the same as your final expression of by substituting for the values of a, y, z.

I used a = 10 because this base is solvable by using the LOG function of the calculator.

I let y = 7
I let z = 15

I got the same answer for the original expression and the final expression which says that I made the translation correctly.

RELATED QUESTIONS
Express as a single logarithm, and, if possible, simplify. 1/4 loga x+8 loga y-2loga... (answered by stanbon)

Express as a single logarithm, and if possible, simplify. Loga x3 � 2 loga... (answered by eshomali)

Express the following as a single logarithm and simplify. • 3/4 loga x - 1/2 loga... (answered by Theo)

Express loga X2 - 2 loga Square root of X as a single logarithm. Simplify if possible. (answered by lwsshak3)

Express as a single logarithum, and, if possible, simplify. 1/4 loga x + 6 loga y - 2... (answered by MathLover1)

Express as a single logarithm, and, if possible, simplify. 1/4loga x+8loga y-2loga x (answered by Fombitz)

express as equivalent expression that a single logarithm and if possible simplify ('a'... (answered by Fombitz)

Express as a single logarithm. loga 7 + loga 12 (answered by rapaljer,Earlsdon)

Express as an equivalent expression that is a single logarithm and if possible simplify (answered by jsmallt9)