Wondering the answers to these:

Find the value of each of the following. Leave your answers as fractions where appropriate.

[I did these myself but need to answer-check]

a) log[base4](1/8)

b) 10^(-10log3)

c) 2log[base3](9)

d) log[base3](3)^(2x)

ans:

a) -3/2

b)(1/3)^10

c) 4

d)3x

These may be wrong, please give me feedback, thx

a) corrrect

b) 10^(-10log3)
= 10^(log3^-10
= 3^-10 ...... using the property a^logak = k

c) correct

d) log3 3^(2x)
= 2x log3 3
= 2x(1)
= 2x

656÷566

To check the answers to these equations, we can use some properties of logarithms and exponents. Let's go through each equation one by one:

a) log[base4](1/8)
To find the value of this logarithm, we need to determine to which power we need to raise the base (4) to obtain the given number (1/8). In other words, we need to solve the equation 4^x = 1/8. Since 1/8 can be written as 2^(-3), we have 4^x = 2^(-3). Converting both sides to the same base, we get (2^2)^x = 2^(-3), which simplifies to 2^(2x) = 2^(-3). By matching the exponents, we have 2x = -3. Therefore, x = -3/2. So the answer is -3/2.

b) 10^(-10log3)
To simplify this expression, we can use the property that 10^log(a) = a. So we have 10^(-10log3) = 1/(10^10log3). Simplifying further, we can rewrite 10^10log3 as (10^log3)^10, which equals 3^10. Therefore, the answer is (1/3)^10.

c) 2log[base3](9)
To find the value of this logarithm, we can use another property of logarithms, which states that log(a^b) = b * log(a). Applying this property, we have 2log[base3](9) = log[base3](9^2) = log[base3](81). Since 81 = 3^4, the answer is 4.

d) log[base3](3)^(2x)
In this equation, we have a logarithm with an exponent. The power rule of logarithms states that log(a^b) = b * log(a). Applying this rule, we can rewrite the expression as 2x * log[base3](3). Since log[base3](3) is equal to 1 (since 3^1 = 3), we are left with 2x * 1, which simplifies to 2x. Therefore, the answer is 2x.

Based on these explanations, your answers seem to be correct:
a) -3/2
b) (1/3)^10
c) 4
d) 2x

However, it's always a good idea to double-check your work and make sure you haven't made any mistakes along the way.