HI THE QUESTION STATES THAT ONE SHOULD CALCULATE THE LOGS WITHOUT THE USE OF A CALCULATOR...OKAY MY PROBLEM IS THIS...
2 3
2log 8 + 2log 8
what should i do? i had come to the piont of...
4 5
log 8 + log 8
But what's to do now i don't know..Think u can help?...
cheers
michelle
Isn't the log 8 = 3log2? You should have log 2 memorized, .3010.
Memorize these logs: log (base 10) 2, and log (base e) 2.
thanx
log3(2x+1)=log3(3x-6)
To simplify the expression 2log8 + 2log8, you can use the property of logarithms which states that log(a) + log(b) = log(a * b). Applying this property, we can simplify the expression as follows:
2log8 + 2log8 = log8^2 + log8^2
Now, we can further simplify this expression by using the property of logarithms that states log(a^b) = b * log(a). Applying this property, we have:
log8^2 + log8^2 = 2 * log8 + 2 * log8
Since log8 is the same as log(base 10) 8, we can evaluate log8 as log(base 10) 8 = log(base 10) 2^3 = 3 * log(base 10) 2.
Now we substitute log8 with 3 * log(base 10) 2:
2 * log8 + 2 * log8 = 2 * (3 * log(base 10) 2) + 2 * (3 * log(base 10) 2)
Simplifying further:
2 * (3 * log(base 10) 2) + 2 * (3 * log(base 10) 2) = 6 * log(base 10) 2 + 6 * log(base 10) 2
Combining like terms:
6 * log(base 10) 2 + 6 * log(base 10) 2 = 12 * log(base 10) 2
So, the simplified expression is 12 * log(base 10) 2.
If you want to evaluate this expression without a calculator, you can use the fact that log(base 10) 2 is approximately 0.3010. Multiplying 0.3010 by 12, we get approximately 3.612.
Therefore, the value of 2log8 + 2log8 is approximately 3.612.