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1955 AHSME Problems/Problem 17: Difference between revisions

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Created page with "If <math>\log x-5 \log 3=-2</math>, then <math>x</math> equals: <math>\textbf{(A)}\ 1.25\qquad\textbf{(B)}\ 0.81\qquad\textbf{(C)}\ 2.43\qquad\textbf{(D)}\ 0.8\qquad\textbf{(..."
 
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<math>x=\boxed{\textbf{(C) }2.43}</math>
<math>x=\boxed{\textbf{(C) }2.43}</math>
==See Also==
==See Also==
Go back to the rest of the [[1955 AHSME Problems]]
{{AHSME 50p box|year=1955|num-b=16|num-a=18}}


{{MAA Notice}}
{{MAA Notice}}

Latest revision as of 09:45, 15 February 2021

If $\log x-5 \log 3=-2$, then $x$ equals:

$\textbf{(A)}\ 1.25\qquad\textbf{(B)}\ 0.81\qquad\textbf{(C)}\ 2.43\qquad\textbf{(D)}\ 0.8\qquad\textbf{(E)}\ \text{either 0.8 or 1.25}$

Solution

Definitions and Properties

$\log n$ is defined as the value of $x$ that satisfies the equation $n = 10^x$. Note that other bases can be applied as well, so $\log_b n$ would be defined as the answer to $n = b^x$

$y \log n = \log n^y$

$\log x - \log y = \log (x / y)$

Learn more properties here: [[1]]

Solving the Equation

$\log x-5 \log 3=-2$

$\log x- \log 3^5=-2$

$\log x- \log 243 =-2$

$\log x / 243 = -2$

$x/243 = 10^{-2}$

$x=\frac{243}{100}$ $x=\boxed{\textbf{(C) }2.43}$

See Also

1955 AHSC (Problems • Answer Key • Resources)
Preceded by
Problem 16 		Followed by
Problem 18
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All AHSME Problems and Solutions


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