Question 1149883
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Use parentheses where required!<br>
What you wrote; surely not what you intended: "49^x-1 = 7*sqrt(7)" --> {{{49^x-1 = 7*sqrt(7)}}}<br>
What you undoubtedly meant: "49^(x-1) = 7*sqrt(7)" --> {{{49^(x-1) = 7*sqrt(7)}}}<br>
In the correct form, the equation is easily solved by expressing both sides of the equation as powers of 7:<br>
{{{49^(x-1) = 7*sqrt(7)}}}
{{{(7^2)^(x-1) = 7*7^(1/2)}}}
{{{7^(2x-2) = 7^(3/2)}}}<br>
The bases are the same; if the expressions are equal, then the exponents are equal.<br>
{{{2x-2 = 3/2}}}
{{{2x = 2+3/2 = 7/2}}}
{{{x = 7/4}}}<br>