Question

What’s the answer to the top question and steps how to solve?

Answer 1

Answer:

-3.69

Step-by-step explanation:

Exponential equations can be solved by taking Ln (natural logarithm) of both sides. The rule we need to know is:

$Ln(a^b)=bLn(a)$

Now lets work out this problem:

$16^{2x+3}=13^{x-1}\\Ln(16^{2x+3})=Ln(13^{x-1})\\(2x+3)Ln(16)=(x-1)Ln(13)$

Using calculator, we take the values of Ln 16 and Ln 13 as:

Ln 16 = 2.7726

Ln 13 = 2.5649

Now, we can solve for x:

$(2x+3)Ln(16)=(x-1)Ln(13)\\(2x+3)2.7726=(x-1)2.5649\\5.5452x+8.3178=2.5649x-2.5649\\2.9803x=-10.8827\\x=-3.69$

x is -3.69 (rounded to 2 decimal places)