Consider the exponential equation. \(\displaystyle{9}^{{x}}={733}\) a. Find x

Sage Fry

Sage Fry

Answered question

2022-03-28

Consider the exponential equation. 9x=733
a. Find x in exact form: x=b. Approximate x, correct to at least 3 decimal places: x=
b. Approximate x, correct to at least 3 decimal places: x=

Answer & Explanation

Laylah Hebert

Laylah Hebert

Beginner2022-03-29Added 15 answers

Exponential equation: - We know that exponents are nothing more than logarithms, and vice versa. As a result, a logarithmic equation can be converted from an exponential equation. This aids in the solution of an exponential equation with multiple bases. The formula for converting exponential equations to logarithmic equations is given below.
bx=a
logba=x
Given: - The exponential equation is, 9x=733
(a) To find: - The exact from of x,
Given that the equation is,
9x=733
Taking log From both sides,
log[9x]=log(733)
Using the logarithmic properties: logax=xloga
xlog(9)=log(733)
x=log(733)log(9)
Thus, the exact from the given equation is,
x=log(733)log(9)
Brendon Stein

Brendon Stein

Beginner2022-03-30Added 5 answers

(b) To find: - Approximate x, correct to at least 3decimal places:
Given that the equation is,
9x=733
The exact form the given equation is,
x=log(733)log(9)
Using the logarithmic value: log(733)=2.8651 and log(9)=0.9542
x=2.86510.9542
=3.0026
Therefore, Approximate x, at least3 decimal place:
x=3.002

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