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Chapter 10: Q. 263 (page 1045)

In the following exercises, use the Properties of Logarithms to condense the logarithm. Simplify if possible.

log4+log25

Short Answer

Expert verified

On simplifying the expression we get,

2

Step by step solution

01

Step 1. Given information 

We are given an expression,

log4+log25

Use the logarithm properties to condense the given expression.

02

Step 2. Identify the logarithm property  

Use product rule of logarithm,

logaM+logaN=loga(M路N)

03

Step 3. Simplifying the expression 

Using the product rule of logarithm, we get

log4+log25=log10(4路25)log4+log25=log10100log4+log25=log10102

Using logaab=b, we get

log4+log25=2

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Most popular questions from this chapter

Convert from exponential to logarithmic form:

32x=324.

Convert from exponential to logarithmic form:

17x=175.

In the following exercises, determine whether or not the given functions are inverses.
f(x)=x+8andg(x)=x-8

In the following exercises, graph each exponential function:

f(x)=3x+2

On the same coordinate system, graph:

f(x)=2x

g(x)=2x-1
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