# Math Help - Remove the logs

1. ## Remove the logs

Could someone help me out with answering these questions:

Remove the logs:
1. logT = -0.0051 log t + 1.7705
2. log T = 0.0046 log t + 1.7202

It's pretty urgent, so any help would be appreciated.

T = temperature
t = time
They're both subbed in values only relevant to my assignment, so they have no value.

2. Let's look at the first one...

Recall the logarithm properties:

Alog(B) = $\log{(B^A)}$
log(A) - log(B) = log(A/B)

So, we have:

$\log{(T)} = -0.0051\log{(t)} + 1.7705$

Using the first property:

$\log{(T)} = \log{(t^{-0.0051})} + 1.7705$

Now, we move all of the logarithms to the same side:

$\log{(T)} - \log{(t^{-0.0051})} = 1.7705$

Now, we use the second property:

$\log{\left(\frac{T}{t^{-0.0051}}\right)} = 1.7705$

$\log{(Tt^{0.0051})} = 1.7705$

Can you finish from here?

The second problem is done similarly.