Convert to Logarithmic equations.
10. 4^-3 =1/64 I have the answer as log4 1/64 =-3
11. 144^1/2 =12 I have the answer as
log 144^12 =1/2
Are these answers right?
I must admit I'm not sure what you are doing but if I converted
4^-3 = 1/64 to a log equation, I would write
-3*log 4 = log(1/64).
I don't know what your answer means as
log4 1/64 = -3 since the 1/64 is just dangling out there by itself with nothing to tell me what you want to do with it.
and for 144^1/2 = 12 I would write
1/2*log 144 = log 12
By the way, when you post problems, be careful that the NUMBER of the problem doesn't run into the problem. For example, the first problem I kept reading as 10.4^-3 = 1/64
Thanks.
I have a question the formula that I used was b^y=x means that logbx=y
is this the correct formula?
so using that formula I got the following.
4^-3 =1/64 I have the answer as log4 1/64 =-3
144^1/2 =12 I have the answer as
log 144^12 =1/2
yes, you are right
if by = x then logbx = y
that is the basic definition of a logarithm
So then are these answers right?
10.) 4^-3 =1/64 I have the answer as log4 1/64 =-3
11.) 144^1/2 =12 I have the answer as
log 144^12 =1/2
I don't like the way you wrote it as
log 144^12 =1/2
the ^ we use as an exponent sign, there is no exponent involved
should have been
log144 12 = 1/2
Yes, your answers are correct.
To convert the equations to logarithmic form, you need to understand the relationship between exponential equations and logarithmic equations. The general form of an exponential equation is a^b = c, where "a" is the base, "b" is the exponent, and "c" is the result. The logarithmic form of this equation is loga(c) = b.
Let's go through each conversion step-by-step.
For the equation 4^-3 = 1/64:
Step 1: Identify the base, exponent, and result.
Base (a) = 4
Exponent (b) = -3
Result (c) = 1/64
Step 2: Rewrite the equation in logarithmic form.
log4(1/64) = -3
So, log4(1/64) = -3 is the correct logarithmic form of the given equation.
For the equation 144^(1/2) = 12:
Step 1: Identify the base, exponent, and result.
Base (a) = 144
Exponent (b) = 1/2
Result (c) = 12
Step 2: Rewrite the equation in logarithmic form.
log144(12) = 1/2
Thus, log144(12) = 1/2 is the correct logarithmic form of the given equation.