Numbers raised to logarithmic expressions I'm currently 11th grader in secondary school and we are learning logarithms. I think I know them quite well but I'm stuck on this exercise: Evaluate 2^x−10^y, where x=1/log6(2) and y=2/log2(10).

Tessa Peters

Tessa Peters

Answered question

2022-10-28

Numbers raised to logarithmic expressions
I'm currently 11th grader in secondary school and we are learning logarithms. I think I know them quite well but I'm stuck on this exercise:
Evaluate 2 x 10 y , where x = 1 / l o g 6 ( 2 ) and y = 2 / l o g 2 ( 10 )
When I plug the values in the calculator I get an answer of 10. But can someone show me the algorithm on how to calculate this? Because I'm unable to get the answer by myself (Sorry if some terms are not on point, I'm not a native English speaker.)

Answer & Explanation

Rylan White

Rylan White

Beginner2022-10-29Added 10 answers

Given
x = 1 log 6 ( 2 ) = log 2 ( 6 )
and
y = 2 log 2 ( 10 ) = 2 log 10 ( 2 ) = log 10 ( 2 ) 2 = log 10 ( 4 )
Now
2 x 10 y = 2 log 2 ( 6 ) 10 log 10 ( 4 ) = 6 4 = 2
Above we have used the formula
log a ( b ) × log b ( a ) = 1
and
n × log e ( m ) = log e ( m ) n
and
a log a ( x ) = x

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