  # How To Condense Logarithms

How To Condense Logarithms. What we need is to condense or compress both sides of the equation into a single log expression. Teaching resources @ www.tutoringhour.com condensing logarithmic expressions 1 3 3 2 1 3 1 2 1) log a m + log a n 3) (log a 2 + 2 log a t) 2) 3(3 log 3 u ± 2 log 3 v) 4) log 4 g ± log 4 h 5) 5 log 5 x + 6.

Identify terms that are products of factors and a logarithm, and rewrite each as the logarithm of a power. In our next few examples we will use a combination of logarithm rules to condense logarithms. Apply the quotient property last.

### In Fact, Logarithm With Base 10 Is Known As The Common Logarithm.

Test how well you can bring into play the product rule, quotient rule, and power rule of logs. We can then group the last two terms and apply the product rule to combine the two. Apply the quotient property last.

### In Our Next Few Examples We Will Use A Combination Of Logarithm Rules To Condense Logarithms.

Log + log + log. Identify terms that are products of factors and a logarithm, and rewrite each as the logarithm of a power. We take the number before the logarithm and raise the exponent of the logarithm to its power.

### What We Need Is To Condense Or Compress Both Sides Of The Equation Into A Single Log Expression.

Rewrite differences of logarithms as the logarithm of a quotient. 9) 5log 3 11 + 10log 3 6 10) 6log 9 z + 1 2 × log 9 x 11) 3log 4 z + 1 3 × log 4 x12) log 6 c + 1 2 × log 6 a + 1 2 × log 6 b 13) 6log. A\log_{b}\left(x\right)=\log_{b}\left(x^a\right), where abs(a)=x, a=x, b=10 and x=27.

### A\Log_{B}\Left(X\Right)=\Log_{B}\Left(X^a\Right), Where Abs(A)=X, A=X, B=10 And X=3.

Justify each step by stating the logarithm property used. Use the product and quotient properties of logarithms, if needed, to expand the logarithm. Use the product property of logarithms,.

### Rewrite The Square Root As An Exponent Of 12.

Expanding and condensing logarithms | worksheet #2. Use the quotient property of logarithms,. Condense the logarithmic expression log(10,3)x+log(10,27)x.