solve for x
log4 64+ log2 2
________________ =x
log3 81
4^3 = 64, so log464 = 3
2^1 = 2, so log22 = 1
3^4 = 81, so log381 = 4
and you end up with
3+1
------ = x
4
x=1
Slove paper
To solve for x in the equation:
(log4 64 + log2 2) / log3 81 = x
We can simplify the equation by evaluating each logarithm expression:
Logarithm properties used:
1. log a + log b = log (a * b)
2. log a (b) = log c (b) / log c (a) [Change of base formula]
Using property 1:
(log4 64 + log2 2) / log3 81
= log4 (64 * 2) / log3 81
Evaluating the logarithmic expressions:
= log4 128 / log3 81
= log(2^7) / log3 (3^4)
= 7log2 2 / 4log3 3
Simplifying further:
= 7 * 1 / 4 * 1
= 7/4
Therefore, x = 7/4.
To solve for x in the given equation:
Step 1: Simplify each logarithmic expression inside the numerator and denominator using the properties of logarithms.
log4 64 = log4 (4^3) = 3
(log2 2 = log2 (2^1) = 1
log3 81 = log3 (3^4) = 4
After simplification, the equation becomes:
(3 + 1) / 4 = x
Step 2: Evaluate the numerator and denominator separately.
3 + 1 = 4
4 is already the numerator, so no further evaluation is needed.
Step 3: Simplify the expression.
4 / 4 = 1
Therefore, x = 1.