# SOLUTION: Will donate. Please help solve two problems. 1.Use the properties of logarithms to write the following expression as a single logarithm: {{{2*log(x)+2*log(y)-4*log(z)}}} 2.Use

Algebra ->  Algebra  -> Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Will donate. Please help solve two problems. 1.Use the properties of logarithms to write the following expression as a single logarithm: {{{2*log(x)+2*log(y)-4*log(z)}}} 2.Use      Log On

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 Algebra: Logarithm Solvers Lessons Answers archive Quiz In Depth

 Click here to see ALL problems on logarithm Question 114077: Will donate. Please help solve two problems. 1.Use the properties of logarithms to write the following expression as a single logarithm: 2.Use the properties of logarithms to expand the expression as much as possible: Found 2 solutions by stanbon, Edwin McCravy:Answer by stanbon(57984)   (Show Source): You can put this solution on YOUR website!1.Use the properties of logarithms to write the following expression as a single logarithm: 2 log x+2 log y-4 log z --------- = log x^2 + log y^2 -logz^4 = log[x^2*y^2/z^4] ======================================= 2.Use the properties of logarithms to expand the expression as much as possible:((( log (3, 81z/y^3x^4) ))) --------- Comment: Keep in mind that all logs are base 3. ---------------- log [81z/y^3x^4)] = log 81 + logz -[logy^3+logx^4] = log81 + logz - 3logy -4logx ------ Applying base 3 where you can: ------ = 4 +logz -3logy - 4logx ============================ Cheers, Stan H. Answer by Edwin McCravy(8999)   (Show Source): You can put this solution on YOUR website!Will donate. Please help solve two problems. 1.Use the properties of logarithms to write the following expression as a single logarithm: 2.Use the properties of logarithms to expand the expression as much as possible: ``` Here are the properties of logarithms we need. Notice that the "A" and "B" properties are the same except that the left and right sides are switched. We need the "B" properties to write as a single logarithm, and the "A" properties to expand a logarithm expression: Property 1A: Property 1B: Property 2A: Property 2B: Property 3A: Property 3B: Property 4: ----------------------------------------------------- 1.Use the properties of logarithms to write the following expression as a single logarithm: Use Property 3B on each of the three terms: Use Property 1B on the first two terms: Use Property 2B on that That is a single logarithm. ---------------------------------------- 2.Use the properties of logarithms to expand the expression as much as possible: Use Property 2: Use Property 1 on both terms, but be sure to enclose the 2nd in parentheses since it is preceded by a minus sign: Remove the parentheses: Use Property 3 on the third and fourth terms: Write as Use Property 4 on the first term That's as far as it will expand. Edwin```