1.Log4^1/8=?
2.log100^0.001=?
3.log8^0.00625=?
Please help me, I can't solve them.
recall that log(a^n) = m*loga
so now just do the multiplications.
Sure! I can help you with these logarithmic problems.
1. To solve the equation log4^(1/8), we need to understand that logarithms are the inverse of exponential functions. In other words, log4^(1/8) asks "What power do we need to raise 4 to in order to get 1/8?" To solve it, we need to rewrite 1/8 as a power of 4.
Since we know that 4^(-1) is equal to 1/4, therefore (1/4)^2 is equal to 1/16. So 4^(-2) is equal to 1/16. So, we can rewrite 1/8 as 4^(-3).
Therefore, log4^(1/8) is equal to -3.
2. To solve log100^(0.001), we again need to understand that logarithms are the inverse of exponential functions. In this case, log100^(0.001) asks "What power do we need to raise 100 to in order to get 0.001?"
To solve it, we need to rewrite 0.001 as a power of 100. We can express 0.001 as 100^(-1/3).
Therefore, log100^(0.001) is equal to -1/3.
3. To solve log8^(0.00625), we again need to understand that logarithms are the inverse of exponential functions. In this case, log8^(0.00625) asks "What power do we need to raise 8 to in order to get 0.00625?"
To solve it, we need to rewrite 0.00625 as a power of 8. We can express 0.00625 as 8^(-2/5).
Therefore, log8^(0.00625) is equal to -2/5.
I hope this helps! Let me know if you have any further questions.