Respuesta :

edisonlara1212

Answer:

approximately 1.2863

Step-by-step explanation:

Ok, so let's just take the log base 3 of both sides, this gets you:

[tex]6x+4=log_34^{x+8}[/tex]

And as you may now, the logarithmic power rule where: [tex]c\ log_ba=log_ba^c[/tex] which works both ways, so we can move the exponent to the front:

[tex]6x+4=(x+8)*log_34[/tex]

Now we can evaluate log base 3 of 4, using a calculator if it allows you to write a custom base, otherwise you can use the change of base formula to write it as a fraction using base 10: [tex]log_34=\frac{log(4)}{log(3)}[/tex]

We get the approximate value of:

[tex]6x+4=(x+8)*1.2618595[/tex]

Distributing this we get:

[tex]6x+4=1.2618595x+10.094876057[/tex]

Now subtract 10.094876057 from both sides

[tex]6x-6.0948760571=1.2618595x[/tex]

Now subtract 6x from both sides

[tex]-6.0948760571=-4.7381405x[/tex]

Divide both sides by -4.7381405

[tex]x\approx1.2863[/tex]

semsee45

Answer:

[tex]x=\dfrac{16 \ln 2 - 4 \ln 3}{6 \ln 3 - 2\ln 2}[/tex]

Step-by-step explanation:

Given equation:

[tex]3^{6x+4}=4^{x+8}[/tex]

Take natural logs of both sides of the equation:

[tex]\implies \ln 3^{6x+4}= \ln 4^{x+8}[/tex]

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

[tex]\implies (6x+4) \ln 3 = (x+8) \ln 4[/tex]

Expand the brackets:

[tex]\implies 6x \ln 3 + 4 \ln 3 = x \ln 4 + 8 \ln 4[/tex]

Collect like terms:

[tex]\implies 6x \ln 3 - x \ln 4 = 8 \ln 4 - 4 \ln 3[/tex]

Factor out x from the left side of the equation:

[tex]\implies x(6 \ln 3 - \ln 4 )= 8 \ln 4 - 4 \ln 3[/tex]

Isolate x:

[tex]\implies x=\dfrac{8 \ln 4 - 4 \ln 3}{6 \ln 3 - \ln 4}[/tex]

Rewrite ln 4 as ln 2² :

[tex]\implies x=\dfrac{8 \ln 2^2 - 4 \ln 3}{6 \ln 3 - \ln 2^2}[/tex]

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

[tex]\implies x=\dfrac{16 \ln 2 - 4 \ln 3}{6 \ln 3 - 2\ln 2}[/tex]

Learn more about log laws here:

https://brainly.com/question/28016999

https://brainly.com/question/27977096

Otras preguntas