How do you simplify this expression?
It gets confusing b/c of logs and exponents. Can someone help me explain how to do this.
8^log(8)x
got confused with this one too.
9^x =57
At first I square rooted but idk what to do now
^ and log are inverse operations
x+8 - 8 = x
x/8 * 8 = x
(√x)^2 = x
log88x = x
8log8x = x
The thing that makes logs initially so confusing is the notation. If we had a cute symbol like + or / or √ things would be a lot easier.
The definition of log8x is that power of 8 which we need to get x.
Now, 9^x = 57 is a bit trickier. Recall that
log9N is the power of 9 you need to get N. So,
log957 is the power of 9 you need to get 57.
Taking log9 of both sides gives you
log99x = log957
But since log99x = x, you end up with
x = log957
So what is the simplified expression of 8^log(8)x? I got confused.
8^log(8)x = x
I stated it clearly as one of the examples.
Similarly, log(8) 8^x = x
To simplify the expression 8^(log(8)*x), you can use the properties of logarithms and exponents.
1. Start by understanding the properties of logs:
a. log(a^b) = b * log(a)
b. log(a^b) = b * log(a) implies that a^b = 10^(b * log(a))
2. Now let's simplify the expression step by step:
a. Rewrite the expression as (10^log(8))^x.
- By the property in step 1b, 8 can be converted to 10 with the base 10 logarithm.
b. Simplify further: 10^(log(8) * x).
- Apply the property in step 1a.
c. Simplify the exponent: 10^(x * log(8)).
Therefore, 8^(log(8)*x) can be rewritten as 10^(x * log(8)).