Evaluate log base10 raise to the power of 350+log base10 raise to the power of 105-log base10 raise to the power of 84
again, this makes no sense.
I agree with bobpursley that your wording makes no sense.
Did you simply mean:
log10 350 + log10 105 - log10 84 ??
That would become
log10 (350*105/84)
= log10 437.5
or simply log 437.5
btw, if the base of the log is 10, it does not have to be stated, so
if I say log10 56, I could just say log 56.
To evaluate the expression log base10 raised to the power of 350 + log base10 raised to the power of 105 - log base10 raised to the power of 84, follow these steps:
1. Apply the logarithmic properties. According to the properties of logarithms, log(base a)M + log(base a)N - log(base a)P = log(base a)(M*N/P). In our case, M = 10^350, N = 10^105, and P = 10^84.
2. Simplify the expression using the properties of indices. In this case, 10^a * 10^b = 10^(a+b) and 10^a / 10^b = 10^(a-b).
Applying these properties, we get:
log(base10) (10^350) + log(base10) (10^105) - log(base10) (10^84)
= 350 + 105 - 84
= 371.
Therefore, the value of log(base10) raised to the power of 350+log(base10) raised to the power of 105-log(base10) raised to the power of 84 is 371.