Algebra?

Algebra Level 2

What is the largest value of x that satisfies

l o g 10 x + 5 = x − 4 log_{10} x+5=x-4


The answer is 10.

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Isaiah Simeone by isaiah simeone , 23, Australia

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3 solutions

Trevor Arashiro
Sep 25, 2014

log ⁡ ( x ) = x − 9 \log(x)=x-9

1 0 x − 9 = x 10^{x-9}=x

Clearly, x ≥ 9 x\geq9 because all x<9 implies that 10^n=negative. Finally, all values of x>10 cause log(x)<x. Thus x=10.

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Also, I have edited the wording of your problem to reduce possible misunderstanding, please check to make sure I didn't alter the meaning of your question.

Trevor Arashiro - 6 years, 8 months ago

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Agreed, I thought it was Log(x+5)=x-4 initially.

David Baker - 6 years, 7 months ago

"Clearly, x>=9 because all x<9 implies that 10^n=negative" Sorry, but I didn't undestant your justification about the condition that x>=9. Could you explain it again?

Daniel Faria - 6 years, 8 months ago

x − l o g ( x ) = 9. x - log(x) = 9. Thus, x must be 10

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A Suganya
Nov 3, 2014

to cancel log, i took x=10, so, now RHS will be x-4= 10-4 = 6 So the LHS to be 6. Therefore, (log 10 power y) +5 = 6 (where y to be found) hence, y+5 = 6 y=1. and finally x = 10 power 1

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