Question

Which of the following is equivalent to log408 rounded to three decimal places?

Answer 1

A. 0.399

B. 0.498

C. 0.564

D. 1.774

Answer 2

Do you mean
\[\log_{40} 8\]? That's much different than \[\log 408\]!!

Answer 3

yeah thats what i meant

Answer 4

\[\log_{40} 8 = x\]means that \[40^x = 8\]Hopefully you can immediately rule out at least one answer choice by looking at that equation.

Answer 5

Do you remember how to work with fractional exponents?

Answer 6

A fractional exponent of \(1/2\) means the same thing as a square root.

\[25^{\frac{1}{2}} = \sqrt{25} = 5\]

I would note that \(0.498\approx \frac{1}{2}\), so answer B would be true only if \[40^{0.498} \approx 40 ^{\frac{1}{2}} = \sqrt{40} \approx 8\]But \(8*8=64\), so \(\sqrt{40}\ne8\), not even close. \[\sqrt{40} = \sqrt{4*10} = 2\sqrt{10} \approx 2*3.1623 = 6.3246\]

There's really only one answer choice that makes sense, given what we've found so far.