What is the answer to 13log_{10}(10x)=338-xlog_{10}(10) ?

The answer to 13log_{10}(10x)=338-xlog_{10}(10) is x=(13\W_{0}(\frac{ln(10)*10^{25})/(13))}{ln(10)}

Solve for x: 13log_{10}(10x)=338-xlog_{10}(10)

The solution is x=(13\W_{0}(\frac{ln(10)*10^{25})/(13))}{ln(10)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

13 lo g_{10} (10 x) = 338 - x lo g_{10} (10)

x = \frac{13 W _{0} ( \frac{l n ( 10 ) \cdot 1 0 ^{25}}{13} )}{ln ( 10 )}

Decimal Notation

x = 292.93203 \dots

Solution steps

13 lo g_{10} (10 x) = 338 - x lo g_{10} (10)

Divide both sides by

13

lo g_{10} (10 x) = \frac{338 - x lo g _{10} ( 10 )}{13}

Apply log rules

lo g_{10} (10 x) = \frac{338 - x}{13}

f (x) = g (x),

then

a^{f (x)} = a^{g (x)}

1 0^{l o g_{10} (10 x)} = 1 0^{\frac{338 - x}{13}}

Simplify

1 0^{l o g_{10} (10 x)} : 10 x

10 x = 1 0^{\frac{338 - x}{13}}

Solve

10 x = 1 0^{\frac{338 - x}{13}} : x = \frac{13 W _{0} ( \frac{l n ( 10 ) \cdot 1 0 ^{25}}{13} )}{ln ( 10 )}

x = \frac{13 W _{0} ( \frac{l n ( 10 ) \cdot 1 0 ^{25}}{13} )}{ln ( 10 )}

Verify Solutions:

x = \frac{13 W _{0} ( \frac{l n ( 10 ) \cdot 1 0 ^{25}}{13} )}{ln ( 10 )}

True

The solution is

x = \frac{13 W _{0} ( \frac{l n ( 10 ) \cdot 1 0 ^{25}}{13} )}{ln ( 10 )}

2 \cdot lo g_{2} (x) = 4

lo g_{2} (lo g_{3} (lo g_{3} (b))) = 0

ln (x + 4) = - 2

lo g_{10} (0.3 x) = - 2

lo g_{3} (lo g_{10} (9 x) + 12 + 9^{x}) = 2 x

What is the answer to 13log_{10}(10x)=338-xlog_{10}(10) ?
The answer to 13log_{10}(10x)=338-xlog_{10}(10) is x=(13\W_{0}(\frac{ln(10)*10^{25})/(13))}{ln(10)}
Solve for x: 13log_{10}(10x)=338-xlog_{10}(10)
The solution is x=(13\W_{0}(\frac{ln(10)*10^{25})/(13))}{ln(10)}