Question

Please help!! Find the solution for t in the equation:

Answer 1

t = 1.322

Explanation:

4×(2^t) = 10

2^t = 10/4 = 2.5

t = log2(2.5)

now, the logarithm to the base 2 of 2.5 must be larger than 1, as 2.5 is larger than 2.

so, it can be only the 4th answer option.

now, to actually calculate it :

log2(2.5) = log10(2.5) / log10(2) = 1.321928095... ≈

≈ 1.322

we were correct.

Answer 2

t = 1.322

Explanation:

Given equation:

`4(2^t)=10`

Divide both sides by 4:

`\implies (4(2^t))/(4)=(10)/(4)`

`\implies 2^t=2.5`

Method 1

Take natural logs of both sides:

`\implies \ln 2^t = \ln 2.5`

`\textsf{Apply the natural log power law}: \quad \ln x^n=n \ln x`

`\implies t \ln 2 = \ln 2.5`

Divide both sides by ln 2:

`\implies (t \ln 2)/(\ln 2) = (\ln 2.5)/(\ln 2)`

`\implies t= (\ln 2.5)/(\ln 2)`

`\implies t=1.321928095...`

Method 2

`\textsf{Apply log law}: \quad a^c=b \iff \log_ab=c`

`\implies \log 2 (2.5)=t`

`\implies t=1.321928095...`

Solution

Therefore, the solution that is nearest to the exact solution is t = 1.322