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Chapter 4: Problem 121

What question can be asked to help evaluate \(\log _{3} 81 ?\)

Short Answer

Expert verified
The value of \(\log _{3} 81 \) is 4.

Step by step solution

01

Understanding Logarithms

The logarithm \(\log _{3} 81 \) can be represented as an exponentiation where the base is 3 and the result is 81. The exponent is what we're trying to find
02

Breaking Down the Problem

The problem can be broken down into the equation \(3^x = 81\). Hence we need to find a value of 'x' which makes this equation true.
03

Finding the Value

We know that \(3^4 = 81\). Therefore, in the equation \(3^x = 81\), 'x' must be 4.

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Most popular questions from this chapter

Exercises \(134-136\) will help you prepare for the material covered in the next section. $$\text { Solve: } \frac{x+2}{4 x+3}=\frac{1}{x}$$

Evaluate or simplify each expression without using a calculator. $$ e^{\ln 125} $$

Evaluate or simplify each expression without using a calculator. $$ \log 1000 $$

If \(\$ 4000\) is deposited into an account paying \(3 \%\) interest compounded annually and at the same time \(\$ 2000\) is deposited into an account paying \(5 \%\) interest compounded annually, after how long will the two accounts have the same balance? Round to the nearest year.

The figure shows the graph of \(f(x)=\ln x\). Use transformations of this graph to graph each function. Graph and give equations of the asymptotes. Use the graphs to determine each function's domain and range. (GRAPH CANNOT COPY). $$ g(x)=2-\ln x $$
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