Question

PLZ HELP Question 1 (4 points)
Use the properties of logs and the logarithms provided to rewrite the log in terms of the variables given.
log base of 3 10 = A
log base of 3 4= B
log base of 3 11= C
Find log3 363
A. A + B + C
B. 2C + 1
C. B + 2
D. A + 2B​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

Use the properties of logs and the logarithms provided to rewrite the log in terms of the variables given.

$\sf{ log_{3}(10) = A }$

$\sf{ log_{3}(4) = B}$

$\sf{ log_{3}(11) = C }$

Find

$\sf{ log_{3}(363) }$

A. A + B + C

B. 2C + 1

C. B + 2

D. A + 2B

FORMULA TO BE IMPLEMENTED

$\sf{1. \: \: log(xy) = log(x) + log(y) }$

$\sf{2. \: \: \: log( {x}^{n} ) = n \: log(x) }$

EVALUATION

$\sf{ log_{3}(363) }$

$\sf{ = log_{3}(3 \times 121) }$

$\sf{ = log_{3}(3 ) + log_{3}(121) \: \: \bigg(\because \: log(xy) = log(x) + log(y) \bigg) }$

$\sf{ = 1 + log_{3}( 121 ) \: \: \bigg(\because \: log_{x}(x) = 1 \bigg) }$

$\sf{ = 1 + log_{3}( {11}^{2} ) \: \: }$

$\sf{ = 1 + 2 \: log_{3}( 11 ) \: \: \bigg(\because \: log( {x}^{n} ) = n \: log(x) \bigg) }$

$\sf{ = 1 + 2 C }$

$\sf{ = 2 C + 1 }$

FINAL ANSWER

Hence the correct option is B. 2C + 1

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