Question

Expert needed! Need assistance with these 2 math problems so please show full solutions and all calculations you used to get to the final answer. Thanks for stopping by!

Answer 1

1. 2^4.0874628
2. 7

Explanation:

You want 17 written as a power of 2, and the value of the expression ...

3log₂(4) -2log₂(3) +log₂(18)

1. Power of 2

Remembering that a logarithm is an exponent, the exponent of 2 that gives a value of 17 will be the log of 17 to the base 2. The change of base formula is useful here.

`\log_2(17)=(\log(17))/(\log(2))\approx(1.23044892)/(0.301029996)\approx4.0874628\\\\\\\boxed{17=2^(4.0874628)}`

2. Log expression

The rules of logarithms tell you ...

log(ab) = log(a) +log(b)

log(a/b) = log(a) -log(b)

log(a^b) = b·log(a)

Combining the logs into a single logarithm, we have ...

3log₂(4) -2log₂(3) +log₂(18) = log₂(4³) -log₂(3²) +log₂(18)

= log₂(4³·18/3²) = log₂(64·18/9) = log₂(128) = log₂(2⁷)

= 7

The value of the log expression is 7.

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Additional comment

A calculator can help you evaluate log expressions.

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