Respuesta :

reinhard10158

Answer:

t = 1.322

Step-by-step 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.

semsee45

Answer:

t = 1.322

Step-by-step explanation:

Given equation:

[tex]4(2^t)=10[/tex]

Divide both sides by 4:

[tex]\implies \dfrac{4(2^t)}{4}=\dfrac{10}{4}[/tex]

[tex]\implies 2^t=2.5[/tex]

Method 1

Take natural logs of both sides:

[tex]\implies \ln 2^t = \ln 2.5[/tex]

[tex]\textsf{Apply the natural log power law}: \quad \ln x^n=n \ln x[/tex]

[tex]\implies t \ln 2 = \ln 2.5[/tex]

Divide both sides by ln 2:

[tex]\implies \dfrac{t \ln 2}{\ln 2} = \dfrac{\ln 2.5}{\ln 2}[/tex]

[tex]\implies t= \dfrac{\ln 2.5}{\ln 2}[/tex]

[tex]\implies t=1.321928095...[/tex]

Method 2

[tex]\textsf{Apply log law}: \quad a^c=b \iff \log_ab=c[/tex]

[tex]\implies \log 2 (2.5)=t[/tex]

[tex]\implies t=1.321928095...[/tex]

Solution

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

Otras preguntas