Get the answer to "How do you solve 2x=10 ?"

Charles Kingsley

Answered question

2021-12-16

How do you solve

2^{x} = 10

Answer & Explanation

Annie Gonzalez

Beginner2021-12-17Added 41 answers

Explanation:
Use any base logarithm on both sides.

\ln (2^{x}) = \ln (10)

Use the identity

\ln (a^{b}) = \ln (a) b

\ln (2) x = \ln (10)

Divide both sides by

\ln (2)

x = \frac{\ln (10)}{\ln (2)}

Lynne Trussell

Beginner2021-12-18Added 32 answers

Use Definition of Common Logarithm

b^{a} = x

if and only if

\log_{b} (x) = a

x = \log_{2} 10

Use Change of Base Rule:

\log_{b} x = \frac{\log_{a} x}{\log_{a} b}

x = \frac{\log 10}{\log 2}

Use Rule of Ten

\log 10 = 1

x = \frac{1}{\log 2}

RizerMix

Expert2021-12-29Added 656 answers

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
$\ln (2^{x}) = \ln (10)$
NSK $E x p a n d \ln (2^{x})$ by moving x outside the logarithm.
$x \ln (2) = \ln (10)$
Divide each term by $\ln (2)$ and simplify.
$x = \frac{\ln (10)}{\ln (2)}$
The result can be shown in multiple forms.
Exact Form:
$x = \frac{\ln (10)}{\ln (2)}$
Decimal Form:
x=3.32192809...

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