Question

If log8 64 + log5 1/125 + 2log2 8=x. What is the value
of x ?​

Answer 1

Answer:

5

log8 64 = 2

log5 1/125 = -3

2log2 8= 6

2-3+6 = 5

Answer 2

SOLUTION

GIVEN

$\displaystyle \sf{ log_{8}(64) + log_{5} \bigg( \frac{1}{125} \bigg) + 2 log_{2}(8) = x }$

TO DETERMINE

The value of x

FORMULA TO BE IMPLEMENTED

We are aware of the formula on logarithm that

$\sf{1. \: \: \: log( {a}^{n} ) = n log(a) }$

$\sf{2. \: \: log(ab) = log(a) + log(b) }$

$\displaystyle \sf{3. \: \: log \bigg( \frac{a}{b} \bigg) = log(a) - log(b) }$

$\sf{4. \: \: log_{a}(a) = 1}$

EVALUATION

$\displaystyle \sf{ log_{8}(64) + log_{5} \bigg( \frac{1}{125} \bigg) + 2 log_{2}(8) = x }$

$\displaystyle \sf{ \implies log_{8}( {8}^{2} ) + log_{5} \bigg( \frac{1}{ {5}^{3} } \bigg) + 2 log_{2}( {2}^{3} ) = x }$

$\displaystyle \sf{ \implies 2 log_{8}( {8}^{} ) + log_{5} \bigg( {5}^{ - 3} \bigg) + 6 log_{2}( {2}^{} ) = x }$

$\displaystyle \sf{ \implies (2 \times 1) - 3 log_{5} \bigg( 5 \bigg) + (6 \times 1 ) = x }$

$\displaystyle \sf{ \implies 2 - 3 + 6 = x }$

$\displaystyle \sf{ \implies x = 8 - 3}$

$\displaystyle \sf{ \implies x = 5}$

FINAL ANSWER

Hence the required value of x = 5

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ if 2log x base y=6,then the relation between x and y

https://brainly.in/question/27199002

2.If 2log((x+y)/(4))=log x+log y then find the value of (x)/(y)+(y)/(x)

https://brainly.in/question/24081206