Question

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

Answer 1

-3.69

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)