Question

Solve for x by using log. Rounded to hundredth. id="TexFormula1" title="4^{2x-5} =6^{-x+1}" alt="4^{2x-5} =6^{-x+1}" align="absmiddle" class="latex-formula">

Answer 1

Answer: $x=1.91$

Step-by-step explanation:

Given the expression $4^{2x-5} =6^{-x+1}$, apply logarithm to both sides. Then:

$log(4)^{2x-5} =log(6)^{-x+1}$

Remembert that according the the properties of logarithms:

$log(a)^n=nlog(a)$

Then:

$(2x-5)log(4)=(-x+1)log(6)$

Appy distributive property and solve for "x":

$2xlog(4)-5log(4)=-xlog(6)+log(6)\\2xlog(4)+xlog(6)=log(6)+5log(4)\\x(2log(4)+log(6))=log(6)+5log(4)\\\\x=\frac{log(6)+5log(4)}{2log(4)+log(6)}\\\\x=1.91$

Answer 2

Answer:

x = 1.91

Step-by-step explanation:

* We have exponential equation to solve it lets study some rules

- If a^m = a^n ⇒ then m = n

- If a^m = b^m ⇒ then a = b or m = 0

- If a^m = b^n ⇒ log(a^m) = log(b^n) ⇒ m log(a) = n log(b)

* You can use log or ln

* Lets solve the problem

∵ $4^{2x-5}=6^{-x+1}$ ⇒ insert log to both sides

∴ $log(4^{2x-5})=log(6^{-x+1})$

- $log(a^{m})=mlog(a)$

∴ (2x - 5)log(4) = (-x + 1)log(6) ⇒ open the brackets

∴ 2xlog(4) - 5log(4) = -xlog(6) + log(6) ⇒ collect x in one side

∴ 2xlog(4) + xlog(6) = log(6) + 5log(4) ⇒ take x as a common factor

∴ x(2log(4) + log(6)) = log(6) + 5log(4)

- divide both sides by coefficient of x

$x=\frac{log(6)+5log(4)}{2log(4)+log(6)}=1.91$

∴ x = 1.91