1) use the properties of logarithms to simplify the logarithmic expression.

log base 10 (9/300)

log - log 300
log 9 = 2 log 3
log 300 = log 3 + log 100 = log 3+2

I just do not know how to put these together now!

1. 👍
2. 👎
3. 👁
4. ℹ️
5. 🚩
1. log base 10 (9/300)
= log10 (3/100)
= log10(3) - log10(100)
= log10(3) - 2

Further simplification is not possible.

The numerical value is 0.47712 - 2
= -1.52288

1. 👍
2. 👎
3. ℹ️
4. 🚩
2. log a b * log bc * logc a=1

1. 👍
2. 👎
3. ℹ️
4. 🚩

## Similar Questions

1. ### math

mathematically Evaluate without using tables 2 log base 10 raised 2 power 5 + log base 10 36 - log base10 9 that is, 2log10 5 +log 10 36 - log 10 9

2. ### Math

Write each logarithmic expression as a single logarithm: Log 2 + 3 log 1

3. ### Trigonometry

This is a logs question If u=x/y^2, which expression is equivalent to log u? 1) log x + 2 log y 2) 2(log x- log y) 3) 2(log x + log y) 4) log x- 2 log y

4. ### Algebra 2

How is the expression log 32 - log 8 written as a single logarithm? log 4 log 8 log 24 log 40

1. ### logarithm functions

use the properties of logarithms to expand the expression as sum, difference or multiple of logarithms. Simplify. a.log(x^3/2) b.log base4 16a

2. ### Trigonometry

The expression log(x^n/ radical y)is equivalent to 1. n log x - 1/2 log y 2. n log x- 2 log y 3. log (nx) - log (1/2y) 4. log (nx) - log (2y)

3. ### Pre Calculus

Assume that x, y, and a are positive numbers. Use the properties of logarithms to write the expression log a 9 xy in terms of the logarithms of x and y. a. 9logbx+9logby b. 19 l o g b ( x + y ) c. 19 l o g b x + l o g b y d.

4. ### Math

Find the exact solution, using common logarithms, and a two-decimal-place approximation of each solution. log(7x + 4) = 2 + log(2x − 3) Solve the equation. log(x^3) = (log x)^2

1. ### Logs.

Can you please help me with the following log. problems? thanxs! Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. 7^x = 6^(x + 7) this is how far

2. ### Math

Use the properties of logarithms to rewrite and simplify the logarithmic expression. 1.) log(9/300) 2.) log2(4^2 x 3^4)

3. ### Econ math/logarithms

If log with base b (2)=0.39 and log with base b (3)=0.61 evaluate the following. log with base b (8). Simplify your answer. How to start? I thought I am supposed to write log base b 2^3 but I don't seem to get an answer that would

4. ### pre calculous

use the properties of logarithms to write the expression as a sum or difference of logarithms or multiples of logarithms. show your work ln x^2/y^3 Assuming x,y AND z are positive use properties of logariths to write the